Eigenvalues and Characteristic Equation

If  $A=\left[\begin{array}{cc}3& 1\\ -1& 2\end{array}\right]$  then what would be the value of  $A^{-1}$

If $A=\left[\begin{array}{cc}1& 5\\ \lambda & 10\end{array}\right], A^{-1}=\alpha A+\beta I$ and $\alpha +\beta =-2$, then $4{\alpha }^2+{\beta }^2+{\lambda }^2$ is equal to :

$A=\left[\begin{array}{ccc}1& 0& 1\\ 0& 1& 1\\ 0& 1& 0\end{array}\right]$ then $A^2-2A=$

Let matrix $A=\left[\begin{array}{ccc}5& -3& 0\\ -3& 5& 0\\ 0& 0& 2\end{array}\right]$, $X$ be a non-zero matrix of order $3\times 1$ and $c$ be a real number. If $A^{2}X=cAX$. Then the number of distinct values of $c$ is

Let $A$ be a $2\times 2$ matrix with real entries such that zero is the only solution of the equation $\left|A-xI\right|=0$. Then

Let $A$ be a $2\times 2$ matrix with real entries such that zero is the only solution of the equation $det\left(A-xI\right)=0$. Then

Let a matrix $A=\left[\begin{array}{ll}2& 3\\ 1& 2\end{array}\right]$, then it will satisfy the equation

Let $A=\left[\begin{array}{ccc}1& 2& 1\\ 0& 1& -1\\ 3& -1& 1\end{array}\right]$ then $A^{-1}$ is equal to

Consider matrix $A=\left(\begin{array}{ll}2& 1\\ 1& 2\end{array}\right).$
If ${\mathrm{A}}^{-1}=\alpha I+\beta A$ where $\alpha ,\beta \in R,$ then $\alpha +\beta$ is equal to (Where ${\mathrm{A}}^{-1}$ denotes inverse of matrix $A$) -

If $A^3=0$, then $I+A+A^2$ equals

If $A$ is a non-singular matrix and $(A-2 I)(A-4 I)=O,$ then $\frac{1}{6}A+\frac{4}{3}{A}^{-1}=$

Cotyledons are also called-

If $A=\left[\begin{array}{ccc}1& 0& 1\\ 1& 1& 0\\ 0& 1& 0\end{array}\right] \text{and} I=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],$ then $A^{-1}$ equals

If $A^2-A+I=O,$ then the inverse of A is

If $A^2-A+I=0$, then the inverse of $A$ is

If ${\mathrm{A}}^3=\mathrm{ }\mathrm{O}$ , then $\mathrm{I}+\mathrm{A}+{\mathrm{A}}^2$ equals

If $A^2-A+I=0,$then the inverse of $A$ is

The characteristic roots of the matrix$\left[\begin{array}{c}1 0 0\\ 2 3 0\\ 4 5 6\end{array}\right]$are

If $A=\left[\begin{array}{cc}3& 1\\ -1& 2\end{array}\right]$ and$I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, then the correct option is