Learn about identity matrices and about how matrix multiplication relates to real number multiplication (spoiler: the distributive property applies but the commutative property does not!).
Matrix multiplication dimensions
Learn about the conditions for matrix multiplication to be defined, and about the dimensions of the product of two matrices.
Defined matrix operations
Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined.
Intro to identity matrices
Learn what an identity matrix is and about its role in matrix multiplication.
Intro to identity matrix
Just as any number remains the same when multiplied by 1, any matrix remains the same when multiplied by the identity matrix. Learn more from Sal.
Dimensions of identity matrix
Sal explains why the identity matrix is always a square matrix, even though it works with non-square matrices.
Properties of matrix multiplication
Learn about the properties of matrix multiplication (like the distributive property) and how they relate to real number addition.
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).
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).
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.
Using properties of matrix operations
Sal determines which of a few optional matrix expressions is equivalent to the matrix expression A*B*C. This is done using what we know about the properties of matrix addition and multiplication.
Using identity & zero matrices
Sal solves a problem where he has to determine whether unknown matrices are zero or identity to make an equation true.