What is matrix multiplication not?

Matrix multiplication is not commutative, meaning that for two matrices A and B, the product AB is generally not equal to BA. Additionally, matrix multiplication is not defined for matrices of incompatible dimensions; for instance, you cannot multiply a 2x3 matrix by a 3x2 matrix without ensuring the inner dimensions match. Lastly, matrix multiplication does not distribute over addition in the same way as scalar multiplication, as the order of operations can affect the result.