Let \(B^{-1}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\) be the inverse of \(B\)y definitionB \(1=1\) i.e.
\(=\left[\begin{array}{ll}0 & 2 \\ 4 & 3\end{array}\right]\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\)
\(=\left[\begin{array}{cc}0+2 c & 0+2 d \\ 4 a+3 c & 4 b+3 d\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\)quating the terms i.e.
\(0+2 c=1 \cdot c=1 / 2: 2 d=0 . d=0\)
\(4 a+3 c=0.4 a+3\left(\frac{1}{2}\right)=0, a=\frac{-3}{8}\)
\(4 h+3 d=1: \quad 4 b+3(0)=1 . \quad b=1 / 4\)
\(B=\left[\begin{array}{cc}-3 / 8 & 1 / 4 \\ 1 / 8 & 0\end{array}\right]=\frac{1}{8}\left[\begin{array}{cc}-3 & 2 \\ 4 & 0\end{array}\right]\)