91Ó°ÊÓ

Find \(\left[\begin{array}{cc}1 & 3 \\ 3 & 10\end{array}\right]^{-1}\)

If \(A=\left[\begin{array}{ll}5 & 2 \\ 3 & 1\end{array}\right]\), then find \(A^{-1}\).

Find \(A^{-1}\), if the matrix \(A\) is given by \(A=\left[\begin{array}{cc}0.8 & 0.6 \\ -0.6 & 0.8\end{array}\right]\)

For what value of \(k\) the matrix \(A=\left[\begin{array}{cc}2 & k \\ 3 & 5\end{array}\right]\) has no inverse.

If \(A=\left[\begin{array}{cc}2 x & 0 \\ x & x\end{array}\right]\) and \(A^{-1}=\left[\begin{array}{cc}1 & 0 \\ -1 & 2\end{array}\right]\), then find the value of \(x\).

If \(A=\left[\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right]\) be such that \(A^{-1}=k A\), then find the value of \(k\).

\(X\) is an unknown square matrix satisfying the equation \(\left[\begin{array}{cc}1 & 3 \\ 0 & 1\end{array}\right] X=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\). Determine the matrix \(X\).

If \(\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] A\left[\begin{array}{cc}-3 & 2 \\ 5 & -3\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\), then find the matrix \(A\).

Find the inverse of the matrix \(\left.A=\mid \begin{array}{ccc}1 & 2 & -2 \\\ -1 & 3 & 0 \\ 0 & -2 & 1\end{array}\right]\). Verify that \(\left|A^{-1}\right|=\frac{1}{|A|}\).

If \(A=\left[\begin{array}{ll}2 & 5 \\ 1 & 6\end{array}\right]\), find \(A^{-1}\) and verify that \(A^{-1}=-\frac{1}{7} A+\frac{8}{7} I\)