https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/v/minors-and-cofactors 2025-05-22T13:12:03.767544849Z Minors and cofactors In this video, we learn how to find minors and cofactors corresponding to the elements of a determinant. We start off with minors and then understand how we can get cofactors from minors. We look at the multiplying factor and how the power of -1 works. We then practice finding minors and cofactors for a given determinant. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Minors and cofactors In this video, we learn how to find minors and cofactors corresponding to the elements of a determinant. We start off with minors and then understand how we can get cofactors from minors. We look at the multiplying factor and how the power of -1 works. We then practice finding minors and cofactors for a given determinant. https://cdn.kastatic.org/ka-youtube-converted/MmpHau7YyjA.mp4/MmpHau7YyjA.mp4 450 Adjoint of a matrix https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/e/minors-and-cofactors 2025-08-08T02:45:51.78671331Z Minors and Cofactors Minors and Cofactors Ashish Gupta exercise https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/v/finding-determinants-using-cofactors 2025-05-22T13:12:03.767544849Z Finding determinants using cofactors In this video, we learn how to find determinants using cofactors. We first refresh our understanding of minors and cofactors. We then compare the terms in the expression for the determinant with cofactors of the same determinant. Finally, we look at what happens if we pair elements with cofactors from a different row and try to build an intuition for the result. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding determinants using cofactors In this video, we learn how to find determinants using cofactors. We first refresh our understanding of minors and cofactors. We then compare the terms in the expression for the determinant with cofactors of the same determinant. Finally, we look at what happens if we pair elements with cofactors from a different row and try to build an intuition for the result. https://cdn.kastatic.org/ka-youtube-converted/Ehgw0R4ZKT4.mp4/Ehgw0R4ZKT4.mp4 376 Adjoint of a matrix https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/e/finding-determinants-using-cofactors 2025-08-08T02:45:51.78671331Z Finding determinants using cofactors Finding determinants using cofactors Ashish Gupta exercise https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/v/adjoint-of-a-matrix 2025-05-22T13:12:03.767544849Z Adjoint of a matrix In this video, we learn how to find the adjoint of a given matrix. We first find minors corresponding to each element. From the set of minors, we build cofactors. Taking the transpose of the matrix of cofactors gives us the adjoint matrix. We practice finding the adjoint of a given 3x3 matrix. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Adjoint of a matrix In this video, we learn how to find the adjoint of a given matrix. We first find minors corresponding to each element. From the set of minors, we build cofactors. Taking the transpose of the matrix of cofactors gives us the adjoint matrix. We practice finding the adjoint of a given 3x3 matrix. https://cdn.kastatic.org/ka-youtube-converted/wtSjH8YeJs8.mp4/wtSjH8YeJs8.mp4 247 Adjoint of a matrix https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/e/adjoint-of-a-matrix 2025-08-08T02:45:51.78671331Z Adjoint of a matrix Adjoint of a matrix Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:determinants-ncert-new/x6f66cbee9a2f805b:adjoint-of-a-matrix/v/intuition-behind-product-with-adjoint 2025-05-22T13:12:03.767544849Z Intuition behind product with adjoint In this video, we understand what happens when we multiply a matrix with its adjoint. We realise that the resultant is equal to the determinant of the matrix multiplied by the identity matrix irrespective of the order of the multiplication. We finally try to build some intuition for why this works. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Intuition behind product with adjoint In this video, we understand what happens when we multiply a matrix with its adjoint. We realise that the resultant is equal to the determinant of the matrix multiplied by the identity matrix irrespective of the order of the multiplication. We finally try to build some intuition for why this works. https://cdn.kastatic.org/ka-youtube-converted/VJKpei3-2jY.mp4/VJKpei3-2jY.mp4 628 Adjoint of a matrix