Tag: multiplicative inverse of a matrix

$A=\begin{bmatrix} 1&-2&3\7&-8&9\4&-5&6\end{bmatrix}$ the new matrix formed by adding $\ 2^{nd}\ row \ to \ 1^{st} $ row  will be

 A=$\begin{bmatrix} 1&2&3\4&5&6\7&8&9\end{bmatrix}$
The new matrix formed  after interchanging $2^{nd}$ and $3^{rd}$rows  will be 

For a matrix $A \begin{pmatrix} 1& 0 & 0\ 2 & 1 & 0\ 3 & 2 & 1\end{pmatrix}$, if $U _{1}, U _{2}$ and $U _{3}$ are $3\times 1$ column matrices satisfying $AU _{1} = \begin{pmatrix}1\ 0 \ 0
\end{pmatrix}, AU _{2} \begin{pmatrix}2\3 \ 0
\end{pmatrix}, AU _{3} = \begin{pmatrix}2\ 3\ 1
\end{pmatrix}$ and $U$ is $3\times 3$ matrix whose columns are $U _{1}, U _{2}$ and $U _{3}$
Then sum of the elements of $U^{-1}$ is

The inverse of a diagonal matrix is a :

Inverse of $A  = \begin{bmatrix} 1& 3\ 2 & -2\end{bmatrix} $ is equal to?A 

If a matrix A is such that $3{A^3} + 2{A^2} + 5A + I = 0$ , then $A^{-1}$ is equal to

If $A$ is a non zero square matrix of order $n$ with $det\left( I+A \right) \neq 0$, and ${A}^{3}=0$, where $I,O$ are unit and null matrices of order $n\times n$ respectively, then ${ \left( I+A \right)  }^{ -1 }=$

If $A=\begin{bmatrix} 3 & -2 \ 5 & 8 \end{bmatrix}$, then $A^{-1}=$

If the matrix $\begin{bmatrix} 0 & 2\beta & \Upsilon \ \alpha & \beta & -\Upsilon \ \alpha & -\beta & \Upsilon \end{bmatrix}$is orthogonal, then

The inverse of the $\begin{bmatrix}- 1 & 5\ - 3 & 2\end{bmatrix}$ is