Question

Which answer choice shows that the commutative property does not hold for matrix multiplication?

Answer 1

Given:

The matrix statements in the options.

To find:

The answer choice that show the commutative property does not hold for matrix multiplication.

Solution:

We known that matrix multiplication is not commutative. if A and B are two non-zero matrices, then

$AB\neq BA$

Let us assume,

$A=\begin{bmatrix}-1&-8\\-3&-5\end{bmatrix}\text{ and }B=\begin{bmatrix}1&3\\8&5\end{bmatrix}$

According to the above property of the matrix, we get

$\begin{bmatrix}-1&-8\\-3&-5\end{bmatrix}\begin{bmatrix}1&3\\8&5\end{bmatrix}\neq \begin{bmatrix}1&3\\8&5\end{bmatrix}\begin{bmatrix}-1&-8\\-3&-5\end{bmatrix}$

Therefore, the correct option is B.