If $\mathbf{A}^{-1} = \begin{pmatrix} -4 & 1 \\ 0 & 2 \end{pmatrix},$ then find the inverse of $\mathbf{A}^2.$
Question:
If $\mathbf{A}^{-1} = \begin{pmatrix} -4 & 1 \\ 0 & 2 \end{pmatrix},$ then find the inverse of $\mathbf{A}^2.$
Answer:
Let's think step by step.

user
\begin{pmatrix}16 & -2 \\ 0 & 4 \end{pmatrix}
If $\mathbf{A}^{-1} = \begin{pmatrix} -4 & 1 \\ 0 & 2 \end{pmatrix},$ then find the inverse of $\mathbf{A}^2.$
train