### Instruction: If $\mathbf{A}^{-1} = \begin{pmatrix} -4 & 1 \\ 0 & 2 \end{pmatrix},$ then find the inverse of $\mathbf{A}^2.$.### Response: I know that $(\mathbf{A}^{-1})^2 = (\mathbf{A}^2)^{-1}$ by the property of inverse matrices.
So, I just need to square $\mathbf{A}^{-1}$ and that will be my answer.
To square a matrix, I multiply it by itself using the rules of matrix multiplication.