Answer
B is the inverse of A.
Work Step by Step
When there is an inverse of a matrix $A A^{-1} = I$ (the Identity Matrix)
$AB = \begin{bmatrix}1 & -1 \\2 & 3\end{bmatrix} \begin{bmatrix} \dfrac{3}{5} &\dfrac{1}{5} \\ \dfrac{-2}{5} & \dfrac{1}{5}\end{bmatrix} =\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}$
and $BA = \begin{bmatrix} \dfrac{3}{5} &\dfrac{1}{5} \\ \dfrac{-2}{5} & \dfrac{1}{5}\end{bmatrix} \begin{bmatrix}1 & -1 \\2 & 3\end{bmatrix} =\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}$
Since $AB=BA$ equals the identity matrix, B is the inverse of A.
