Find Matrix A by certain operations Given as such:
$4(A^T+2I)^{-1} =$ \begin{bmatrix}1&1\\-3/2&1/2\end{bmatrix}
Now to find Matrix A, would I have to inverse the matrix on the RHS to make it equal to A on the LHS and perform the opposite operations? A little stumped on the operations necessary to get the right result.
Just need some clarification, thanks.

Hints:
Divide both sides by $4$ to get
$$(A^T+2I)^{-1}=\left[\begin{array}{cc}
1/4 & 1/4 \\
-3/8 & 1/8 \\
\end{array}\right]$$
Then take the inverse of both sides:
$$A^T+2I=\left[\begin{array}{cc}
1/4 & 1/4 \\
-3/8 & 1/8 \\
\end{array}\right]^{-1}.$$
I'll leave it to you to find the inverse.
Then subtract $2I$ from both sides:
$$A^T=\left[\begin{array}{cc}
1/4 & 1/4 \\
-3/8 & 1/8 \\
\end{array}\right]^{-1}-2I$$
Lastly, take the transpose of both sides, and note that $(A^T)^T=A$.
