If $\mathbf{A}^{-1} = \begin{pmatrix} 4 & 0 \\ 1 & -1 \end{pmatrix}$ and $\mathbf{B}^{-1} = \begin{pmatrix} 2 & -1 \\ -1 & 3 \end{pmatrix},$ then find the inverse of $\mathbf{A} \mathbf{B}.$
Question:
If $\mathbf{A}^{-1} = \begin{pmatrix} 4 & 0 \\ 1 & -1 \end{pmatrix}$ and $\mathbf{B}^{-1} = \begin{pmatrix} 2 & -1 \\ -1 & 3 \end{pmatrix},$ then find the inverse of $\mathbf{A} \mathbf{B}.$
Answer:
Let's think step by step.

user
\begin{pmatrix} 7 & 1 \\ -1 & -3 \end{pmatrix}
If $\mathbf{A}^{-1} = \begin{pmatrix} 4 & 0 \\ 1 & -1 \end{pmatrix}$ and $\mathbf{B}^{-1} = \begin{pmatrix} 2 & -1 \\ -1 & 3 \end{pmatrix},$ then find the inverse of $\mathbf{A} \mathbf{B}.$
train