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

If the multiplicative group consists of $2 \times 2$ matrices of the form $\begin{bmatrix} a & a \\ a & a \end{bmatrix}$,where $a \neq 0$ and $a \in \mathbb{R}$,then the inverse of $\begin{bmatrix} 2 & 2 \\ 2 & 2 \end{bmatrix}$ is:

Find the inverse of the matrix (if it exists): $\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & \cos a & \sin a \\ 0 & \sin a & -\cos a\end{array}\right]$

If $A(\operatorname{adj} A)=5 I$ where $I$ is the identity matrix of order $3$,then $|\operatorname{adj} A|$ is equal to

Find the inverse of the matrix (if it exists): $\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5\end{array}\right]$

If $A = \begin{bmatrix} 1 & 2 & 0 \\ 0 & 1 & 2 \\ 2 & 0 & 1 \end{bmatrix}$,then find $adj(A)$.