In this video we explore whether matrix multiplication is commutative or whether it really does matter in which order we multiply 2 matrices.
In the first example, we have a row vector A = [4 -2 -3] and a column vector B = [2; 1; 5]. If we multiply A x B we get a 1 x 1 matrix, which is just a number. If we multiply B x A, we get a new 3 x 3 matrix. This is a remarkable result, and is one of the coolest properties of matrix multiplication.
In the second example, we explore why matrix multiplication is generally not commutative even for square matrices.
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