Inverse Matrix

Find the inverse of the following matrix:

$A=\left[\begin{array}{ccc}3& 2& 1\\ 4& -1& 2\\ 7& 3& -3\end{array}\right]$

Find the inverse of the following matrix by using transformation method.$\left[\begin{array}{cc}1& 2\\ 2& -1\end{array}\right]$

If $A$ is an invertible matrix and $B \& C$ are any two matrices such that  $AB=AC$, then it necessarily implies $B=C$

If $\mathrm{A}=\left[\begin{array}{lll}1& 0& 0\\ 0& 1& 1\\ 0& -2& 4\end{array}\right],\mathrm{ }\mathrm{I}=\left[\begin{array}{lll}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$ and ${\mathrm{A}}^{-1}=\frac{1}{6}\left({\mathrm{A}}^2+\mathrm{c}\mathrm{A}+\mathrm{d}\right)$ then the sum of values of $\mathrm{c}$ and $\mathrm{d}$ is

Find the inverse of the following matrix (if exists): $\left[\begin{array}{cc}1& 3\\ 2& 7\end{array}\right]$

If $A=\left[\begin{array}{ccc}x& 0& 0\\ 0& y& 0\\ 0& 0& z\end{array}\right]$ is a nonsingular matrix then find $A^{-1}$ by elementary row transformations.Hence, find the inverse of $\left[\begin{array}{ccc}2& 0& 0\\ 0& 1& 0\\ 0& 0& -1\end{array}\right]$.

Find the inverse of the following matrix by using transformation method.

$\left[\begin{array}{ccc}2& 0& -1\\ 5& 1& 0\\ 0& 1& 3\end{array}\right]$

Find the inverse of the following matrix by using transformation method.

$\left[\begin{array}{ccc}0& 1& 2\\ 1& 2& 3\\ 3& 1& 1\end{array}\right]$

Find the inverse of the following matrix by using transformation method.

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

If $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]$, then prove that $A^2-4A-5I_3=0$ and using this find $A^{-1}$.

If $A=\left[\begin{array}{cc}2& 3\\ 5& -2\end{array}\right]$, then prove that $A^{-1}=\frac{1}{19}A$.

If $A=\left[\begin{array}{cc}-8& 5\\ 2& 4\end{array}\right]$, then prove that $A^2+4A-42I_2=O$ and using this find $A^{-1}$.

If matrix $A=\left[\begin{array}{cc}-8& 5\\ 2& 4\end{array}\right]$, then prove that $A^2+4A-42=0$ and find $A^{-1}$.

Prove that the matrix $A=\left[\begin{array}{cc}2& -3\\ 3& 4\end{array}\right]$ satisfies the equation $A^2-6A+17=0$ and find $A^{-1}$.

Using elementary transformations, find $A^{-1}$, where $A=\left[\begin{array}{ccc}1& 2& -2\\ -1& 3& 0\\ 0& -2& 1\end{array}\right]$. Then the value of first row first column element $\left(a_{11}\right)$ is

Inverse of given matrix $\left[\begin{array}{ccc}2& 3& -3\\ -1& -2& 2\\ 1& 1& -1\end{array}\right]$ ______. (exists / does not exist)

For what value of $k$ the matrix $\left[\begin{array}{ccc}0& 3& k\\ 2& 3& 4\\ 1& 0& -1\end{array}\right]$ is not invertible.

If $A$ is $3\times 3$ invertible matrix, then show that for any scalar $k$ (non-zero), $kA$ is invertible and $(kA{)}^{-1}=\frac{1}{k}{A}^{-1}$.

If $A^{-1}=\left[\begin{array}{ccc}3& -1& 1\\ -15& 6& -5\\ 5& -2& 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}1& 2& -2\\ -1& 3& 0\\ 0& -2& 1\end{array}\right]$, if  $(AB{)}^{-1}=\left[\begin{array}{ccc}9& -3& 5\\ -2& k& 0\\ 1& 0& 2\end{array}\right]$, then the value of $k$.

If $A$ is a invertible square matrix and $k$ is a non-negative real number. then $(kA{)}^{-1}=$?