Let A be an invertible matrix; therefore, if B is its inverse, according to the inverse matrix definition,
[tex]AB=BA=I_{n\times n}[/tex]
Therefore, in our case,
[tex]A=\begin{bmatrix}{5} & {8} \\ {2} & {3}\end{bmatrix},B=\begin{bmatrix}{-3} & {8} \\ {2} & {-5}\end{bmatrix},I_{n\times n}=I_{2\times2}=\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix}[/tex]
Then,
[tex]\begin{bmatrix}{5} & {8} \\ {2} & {3}\end{bmatrix}\begin{bmatrix}{-3} & {8} \\ {2} & {-5}\end{bmatrix}=\begin{bmatrix}{-3} & {8} \\ {2} & {-5}\end{bmatrix}\begin{bmatrix}{5} & {8} \\ {2} & {3}\end{bmatrix}=\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix}[/tex]
Hence, the answers are options B and C
