Solution
= Solution
For the choice of $B$ in part (b)(i), the two-by-two <matrix inverse> formula gives
$$
\boxed{B^{-1}=\frac13\begin{pmatrix}-1&-2\\2&1\end{pmatrix}.}
$$
Multiplication gives $BB^{-1}=B^{-1}B=I$, providing a direct check.
= Solution
For the choice of $B$ in part (b)(i), the two-by-two <matrix inverse> formula gives
$$
\boxed{B^{-1}=\frac13\begin{pmatrix}-1&-2\\2&1\end{pmatrix}.}
$$
Multiplication gives $BB^{-1}=B^{-1}B=I$, providing a direct check.