Inverse Matrix

Find the inverse of the following matrix:

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

Using elementary transformations, find the inverse of the matrix $\left[\begin{array}{cc}3& 10\\ 2& 7\end{array}\right]$.

If $A=\left[\begin{array}{ll}3& 4\\ 1& 2\end{array}\right]$, then $A^{-1}$ is equal to

By using elementary transformations, find the inverse of the matrix $A=\left[\begin{array}{ll}1& 3\\ 2& 7\end{array}\right]$.

Solve the following system of linear equations by matrix method.

$x-y+2z=7$

$3x+4y-5z=-5$

$2x-y+3z=12$

Which is the inverse of the matrix $A=\left[\begin{array}{ccc}\cos \theta & \sin \theta & 0\\ -\sin \theta & \cos \theta & 0\\ 0& 0& 1\end{array}\right]?$

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

If matrix $A=\left[\begin{array}{ll}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$, then find $A^{-1}$

If $A=\left[\begin{array}{ccc}2& 0& -1\\ 5& 1& 0\\ 0& 1& 3\end{array}\right]$ and $A^{-1}=\left[\begin{array}{ccc}3& -1& 1\\ \alpha & 6& -5\\ \beta & -2& 2\end{array}\right]$, then the values of $\alpha$ and $\beta$ are, respectively

If $\left[\begin{array}{ccc}1& -1& x\\ 1& x& 1\\ x& -1& 1\end{array}\right]$ has no inverse, then the real value of $x$ is

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

Let $A$ and $B$ are two non-singular matrices of order $3$ such that $\left|\mathrm{A}\right|=3$ and $A^{-1}{B}^2+2AB=O$, then the value of $\left|A^4-2A^{2}B\right|$ is equal to (where $O$ is the null matrix of order $3$)