Given: Matrix statements in the given options
To determine: The correct answer that shows commutative property does not hold for matrix multiplication
Solution
It is known that matrix multiplication is not commutative. if A and B are two non-zero matrices, then
[tex]AB\ne BA[/tex]
If
[tex]\begin{gathered} A=\begin{bmatrix}{-5} & {8} \\ {1} & {3}\end{bmatrix} \\ B=\begin{bmatrix}{4} & {2} \\ {7} & {9}\end{bmatrix} \\ Then \\ \begin{bmatrix}{-5} & {8} \\ {1} & {3}\end{bmatrix}\begin{bmatrix}{4} & {2} \\ {7} & {9}\end{bmatrix}\ne\begin{bmatrix}{4} & {2} \\ {7} & {9}\end{bmatrix}\begin{bmatrix}{-5} & {8} \\ {1} & {3}\end{bmatrix} \end{gathered}[/tex]
Hence, OPTION C is the correct answer
