Linear Algebra - Inverse Matrices - Finding inverse of A.

Question

I am trying to solve the following problem but unable to come up with a solution.

Question: Find $A^{-1}$ given that $(B^{-1} A)^{-1} = \begin{bmatrix} -1 & 3 & 5 \\ 3 & -2 & 2 \\ 2 & -4 & -7 \\ \end{bmatrix} $ and $B^{-1}= \begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} $.

I will appreciate some help/lead on this problem. Thank you.

Answer 1

Since $(B^{-1}A)^{-1}=A^{-1}B$, you can just multiply the two matrices. That is, $A^{-1}=(B^{-1}A)^{-1}B^{-1}$.