Inverse Matrix

Find the inverse of the following matrix:

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

Let $A=\left[\begin{array}{rrr}2& -1& 1\\ -1& 2& -1\\ 1& -1& 2\end{array}\right]$ and $4B=\left[\begin{array}{rrr}3& 1& -1\\ 1& 3& x\\ -1& 1& 3\end{array}\right]$. If $B$ is the inverse of $A,$ then the value of $x$ is

If $A^T{A}^{-1}$ is symmetric, then $A^2=$

If ${\left(AB\right)}^{-1}=\left[\begin{array}{cc}12& -17\\ -19& 27\end{array}\right]$ and $A^{-1}=\left[\begin{array}{cc}1& -1\\ -2& 3\end{array}\right]$ then $B^{-1}=$

If $A=\left[\begin{array}{ccc}3& 1& -1\\ 2& -2& 0\\ 1& 2& -1\end{array}\right]$ and $A^{-1}=\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]$ then the value of $a_{23}$ is

If $A$ is a $3\times 3$ non-singular matrix such that $A{A}^T=A^{T}A$ and $B=A^{-1}{A}^T$, then $B{B}^T=$

Let $A={\left(a_{ij}\right)}_{1\le i, j\le 3}$ be a $3\times 3$ invertible matrix where each $a_{ij}$ is a real number. Denote the inverse of the matrix $A$ by $A^{-1}.$ If $\sum _{j=1}^3{a}_{ij}=1$ for $1\le i\le 3,$ then

Let $A$ be a $2\times 2$ matrix of the form $A=\left[\begin{array}{ll}a& b\\ 1& 1\end{array}\right],$ where $a, b$ are integers and $-50\le b\le 50.$ The number of such matrices $A$ such that $A^{-1},$ the inverse of $A,$ exists and $A^{-1}$ contains only integer entries is

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 $3$)