Find the adjoint of the given matrix and verify in each case that $A. (adj A)=(adj A).A=m \left|A\right|.I.$

$\left[\begin{array}{ccc}4& 5& 3\\ 1& 0& 6\\ 2& 7& 9\end{array}\right]$

Find the adjoint of the given matrix and verify in each case that $A. (adj A)=(adj A).A=m \left|A\right|.I$.

$\left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0\\ \sin \alpha & \cos \alpha & 0\\ 0& 0& 1\end{array}\right]$

If $A=\left[\begin{array}{ccc}-4& -3& -3\\ 1& 0& 1\\ 4& 4& 3\end{array}\right]$, show that adj $A=A$.

If $A=\left[\begin{array}{ccc}-1& 2& 2\\ -2& 1& -2\\ -2& -2& 1\end{array}\right]$, show that adjoint $A=3A\text{'}$.

Find the inverse of the matrix $\left[\begin{array}{cc}3& -5\\ -1& 2\end{array}\right]$

Find the inverse of the matrices given below.

$\left[\begin{array}{ll}4& 1\\ 2& 3\end{array}\right]$

Find the inverse of the matrix given below.

$\left[\begin{array}{cc}2& -3\\ 4& 6\end{array}\right]$

Find the inverse of the matrices given below.

$\left[\begin{array}{ll}a& b\\ c& d\end{array}\right]$, when $(ab–bc)\ne 0$

Find the inverse of the matrix given below.

$\left[\begin{array}{ccc}1& 2& 5\\ 1& -1& -1\\ 2& 3& -1\end{array}\right]$