Why is matrix multiplication not commutative?

Question

21 Feb 2025

Answer :

Word Count : 318

Matrix multiplication is not commutative, meaning that in general, for two matrices A and B, the product AB does not equal BA. This property arises from the way matrix multiplication is defined and the conditions required for multiplication to be possible.

To understand this, let's consider the dimensions of the matrices involved. For matrix multiplication to be valid, the number of columns in the first matrix must match the number of rows in the second matrix. Therefore, if A _________ __________ _______ ______ _________ ______ ____ _______.
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