(Solved): #6 The Inverse of a Matrix In Exercises 1-6, show that \( B \) is the inverse of \( A \). 1. \( A=\l ...

The Inverse of a Matrix In Exercises 1-6, show that \( B \) is the inverse of \( A \). 1. \( A=\left[\begin{array}{ll}2 & 1 \\ 5 & 3\end{array}\right], \quad B=\left[\begin{array}{rr}3 & -1 \\ -5 & 2\end{array}\right] \) 2. \( A=\left[\begin{array}{rr}1 & -1 \\ -1 & 2\end{array}\right], \quad B=\left[\begin{array}{ll}2 & 1 \\ 1 & 1\end{array}\right] \) 3. \( A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right], \quad B=\left[\begin{array}{rr}-2 & 1 \\ \frac{3}{2} & -\frac{1}{2}\end{array}\right] \) 4. \( A=\left[\begin{array}{rr}1 & -1 \\ 2 & 3\end{array}\right], \quad B=\left[\begin{array}{rr}\frac{3}{5} & \frac{1}{5} \\ -\frac{2}{5} & \frac{1}{5}\end{array}\right] \) 5. \( A=\left[\begin{array}{rrr}-2 & 2 & 3 \\ 1 & -1 & 0 \\ 0 & 1 & 4\end{array}\right], \quad B=\frac{1}{3}\left[\begin{array}{rrr}-4 & -5 & 3 \\ -4 & -8 & 3 \\ 1 & 2 & 0\end{array}\right] \) \( A=\left[\begin{array}{rrr}2 & -17 & 11 \\ -1 & 11 & -7 \\ 0 & 3 & -2\end{array}\right], \quad B=\left[\begin{array}{rrr}1 & 1 & 2 \\ 2 & 4 & -3 \\ 3 & 6 & -5\end{array}\right] \)