https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:multiplying-matrices-by-matrices/v/matrix-multiplication-intro 2021-02-05T04:23:34Z Intro to matrix multiplication Sal explains what it means to multiply two matrices, and gives an example. Sal Khan video https://cdn.kastatic.org/googleusercontent/71DBF4ngxQlt65MbUXVHbcFBRM3LG0Jzq3D5Nazf6kupAAz0nrQa0LzW2PSWe3l2XC3CGBzPkyphsdEPQfcEgPc Intro to matrix multiplication Sal explains what it means to multiply two matrices, and gives an example. https://cdn.kastatic.org/ka-youtube-converted/kT4Mp9EdVqs.mp4/kT4Mp9EdVqs.mp4 386 Multiplication by a matrix https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:multiplying-matrices-by-matrices/v/multiplying-a-matrix-by-a-matrix 2021-03-19T16:21:23Z Multiplying matrices Sal gives an example of a multiplication of two matrices that don't have the same dimensions. Sal Khan video https://cdn.kastatic.org/googleusercontent/BqJmJ2WeHN2rv1MdYS7EpVD5S2f39dWsBMNw1QMTR48in-YiaWuMHzYVFHTwyR7FXwEj3ARgLLf7807AfVoxnK0 Multiplying matrices Sal gives an example of a multiplication of two matrices that don't have the same dimensions. https://cdn.kastatic.org/ka-youtube-converted/OMA2Mwo0aZg.mp4/OMA2Mwo0aZg.mp4 330 Multiplication by a matrix https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:multiplying-matrices-by-matrices/e/multiplying_a_matrix_by_a_matrix 2026-03-24T23:41:07.080866137Z Multiply matrices Find the result of a multiplication of two given matrices. Tomer Gal exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/commutative-property-matrix-multiplication 2021-03-19T16:21:23Z Is matrix multiplication commutative? Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way). Sal Khan video https://cdn.kastatic.org/googleusercontent/WJR2HLZMFiOH6UEMJBxbFA4kAksb7KVyEteoWXm-tMbL6IcnVzmHPrqowjX9sAbnMyXzfCYgo6Otx8iq86bwVWcB Is matrix multiplication commutative? Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way). https://cdn.kastatic.org/ka-youtube-converted/z-SU7P-gIoQ.mp4/z-SU7P-gIoQ.mp4 452 Multiplication by a matrix https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/associative-property-matrix-multiplication 2021-03-19T16:21:23Z Associative property of matrix multiplication Sal shows that matrix multiplication is associative. Mathematically, this means that for any three matrices A, B, and C, (A*B)*C=A*(B*C). Sal Khan video https://cdn.kastatic.org/googleusercontent/pmLLh5x1lgfZvgSJ0tcBps-WRAbPR55vRtP3I4cnQwijpNXwTR8pHIYvToKJNfJo1hRFLxbWThRSnO4U7J5jc-I Associative property of matrix multiplication Sal shows that matrix multiplication is associative. Mathematically, this means that for any three matrices A, B, and C, (A*B)*C=A*(B*C). https://cdn.kastatic.org/ka-youtube-converted/8Ryfe82DTcM.mp4/8Ryfe82DTcM.mp4 517 Multiplication by a matrix https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:matrices-ncert-new/x6f66cbee9a2f805b:multiplication-by-a-matrix/v/distributive-property-of-matrix-multiplication 2025-05-22T13:12:03.767544849Z Distributive property of matrix multiplication In this video, we verify distributive property of multiplication of matrices. Just like scalars, we can mutliply matrices using distributive properties. We first look at a scenario where we have 3x3 matrices. We then pick a scenario where we have 2x2 matrices. Finally, we also observe that A(B+C) is not the same as (B+C)A. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Distributive property of matrix multiplication In this video, we verify distributive property of multiplication of matrices. Just like scalars, we can mutliply matrices using distributive properties. We first look at a scenario where we have 3x3 matrices. We then pick a scenario where we have 2x2 matrices. Finally, we also observe that A(B+C) is not the same as (B+C)A. https://cdn.kastatic.org/ka-youtube-converted/s4P3pID9iX8.mp4/s4P3pID9iX8.mp4 495 Multiplication by a matrix https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/zero-matrix 2021-03-19T16:21:22Z Zero matrix & matrix multiplication Just as any number multiplied by zero is zero, there is a zero matrix such that any matrix multiplied by it results in that zero matrix. Learn more from Sal. Sal Khan video https://cdn.kastatic.org/googleusercontent/i-6W_dqrs-9neFNYpv9PGKBR95MhQqjDY_uKtketTzFi90_TAT9tLgs5G3QHPMrhu4nAMhqKjXNS3Zs18ewF7eyQog Zero matrix & matrix multiplication Just as any number multiplied by zero is zero, there is a zero matrix such that any matrix multiplied by it results in that zero matrix. Learn more from Sal. https://cdn.kastatic.org/ka-youtube-converted/LOf8bfjiLow.mp4/LOf8bfjiLow.mp4 282 Multiplication by a matrix https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:matrices-ncert-new/x6f66cbee9a2f805b:multiplication-by-a-matrix/v/evaluating-expressions-using-matrix-multiplication 2025-05-22T13:12:03.767544849Z Evaluating expressions using matrix multiplication In this video, we learn how to evaluate expressions when a square matrix is given. We first evaluate a quadratic expression using a 2x2 matrix. We then evaluate a cubic expression using a 3x3 matrix. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Evaluating expressions using matrix multiplication In this video, we learn how to evaluate expressions when a square matrix is given. We first evaluate a quadratic expression using a 2x2 matrix. We then evaluate a cubic expression using a 3x3 matrix. https://cdn.kastatic.org/ka-youtube-converted/0TNWN2k56CE.mp4/0TNWN2k56CE.mp4 463 Multiplication by a matrix https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:matrices-ncert-new/x6f66cbee9a2f805b:multiplication-by-a-matrix/e/evaluating-expressions-using-matrix-multiplication 2025-08-08T02:45:51.78671331Z Evaluating expressions using matrix multiplication Evaluating expressions using matrix multiplication Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:matrices-ncert-new/x6f66cbee9a2f805b:multiplication-by-a-matrix/v/applying-trigonometric-identities-to-evaluate-matrices 2025-05-22T13:12:03.767544849Z Applying trigonometric identities to evaluate matrices In this video, we learn how to apply trigonometric identities to evaluate sums and products of matrices. In addition to matrix addition and multiplication properties, we also apply our knowledge from the trigonometry unit to solve these problems. For the problems covered in this video, we appy Pythagorean identity, angle sum property, and half angle identiy. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Applying trigonometric identities to evaluate matrices In this video, we learn how to apply trigonometric identities to evaluate sums and products of matrices. In addition to matrix addition and multiplication properties, we also apply our knowledge from the trigonometry unit to solve these problems. For the problems covered in this video, we appy Pythagorean identity, angle sum property, and half angle identiy. https://cdn.kastatic.org/ka-youtube-converted/J9BHF3s71Go.mp4/J9BHF3s71Go.mp4 516 Multiplication by a matrix https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:matrices-ncert-new/x6f66cbee9a2f805b:multiplication-by-a-matrix/e/applying-trigonometric-identities-to-evaluate-matrices 2025-08-08T02:45:51.78671331Z Applying trigonometric identities to evaluate matrices Applying trigonometric identities to evaluate matrices Ashish Gupta exercise https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:matrices/v/solving-for-matrix-given-product 2025-05-22T13:12:03.767544849Z Solving for matrix given product In this video, we learn how to find one of the matrices if we know the other one and their product. To find a 2x2 matrix, we need to solve 4 equations (for 4 variables). We solve 2 problems in this video. For the second one, we first try to find the order of the missing matrix before solving for its elements. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Solving for matrix given product In this video, we learn how to find one of the matrices if we know the other one and their product. To find a 2x2 matrix, we need to solve 4 equations (for 4 variables). We solve 2 problems in this video. For the second one, we first try to find the order of the missing matrix before solving for its elements. https://cdn.kastatic.org/ka-youtube-converted/5iChvsyS9AQ.mp4/5iChvsyS9AQ.mp4 563 Multiplication by a matrix https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:matrices/e/solving-for-matrix-given-product 2025-08-08T02:45:51.78671331Z Solving for matrix given product Solving for matrix given product Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:matrices-ncert-new/x6f66cbee9a2f805b:multiplication-by-a-matrix/v/conceptual-problems-on-multiplication-of-matrices 2025-05-22T13:12:03.767544849Z Conceptual problems on multiplication of matrices In this video, we solve a conceptual problem that tests our understanding of properties of addition and multiplication of matrices. We try to figure out the restrictions on the number of rows and columns of the given matrix provided that the given expression is defined. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Conceptual problems on multiplication of matrices In this video, we solve a conceptual problem that tests our understanding of properties of addition and multiplication of matrices. We try to figure out the restrictions on the number of rows and columns of the given matrix provided that the given expression is defined. https://cdn.kastatic.org/ka-youtube-converted/a9If9OCr8jM.mp4/a9If9OCr8jM.mp4 339 Multiplication by a matrix https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:matrices-ncert-new/x6f66cbee9a2f805b:multiplication-by-a-matrix/e/matrix-operations-and-order 2026-04-14T11:30:38.220334671Z Matrix Operations and Order Matrix Operations and Order Ashish Gupta exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/a/properties-of-matrix-multiplication 2024-11-04T03:21:18.50878448Z Properties of matrix multiplication Learn about the properties of matrix multiplication (like the distributive property) and how they relate to real number multiplication. article