If $\mathbf{A}^{-1} = \begin{pmatrix} 4 & 6 \\ -2 & 10 \end{pmatrix},$ and $\mathbf{B} = \frac{1}{2} \mathbf{A},$ then find $\mathbf{B}^{-1}.$
Question:
If $\mathbf{A}^{-1} = \begin{pmatrix} 4 & 6 \\ -2 & 10 \end{pmatrix},$ and $\mathbf{B} = \frac{1}{2} \mathbf{A},$ then find $\mathbf{B}^{-1}.$
Answer:
Let's think step by step.

user
\begin{pmatrix} 8 & 12 \\ -4 & 20 \end{pmatrix}
If $\mathbf{A}^{-1} = \begin{pmatrix} 4 & 6 \\ -2 & 10 \end{pmatrix},$ and $\mathbf{B} = \frac{1}{2} \mathbf{A},$ then find $\mathbf{B}^{-1}.$
train