If $A$ is a singular matrix of order $n$,then $A(adj\,A)$ is

If $\omega$ is a complex cube root of unity and $A=\begin{bmatrix} \omega & 0 \\ 0 & \omega \end{bmatrix}$,then $A^{-1}=$

If $A = \begin{bmatrix} e^t & e^{-t} \cos t & e^{-t} \sin t \\ e^t & -e^{-t} \cos t - e^{-t} \sin t & -e^{-t} \sin t + e^{-t} \cos t \\ e^t & 2e^{-t} \sin t & -2e^{-t} \cos t \end{bmatrix}$,then $A$ is:

The adjoint of the matrix $A = \begin{bmatrix} 2 & -3 \\ 3 & 5 \end{bmatrix}$ is

If $A = [a_{ij}]_{3 \times 3}$ is a matrix such that $a_{ij} = |2i - 5j|$, where $|.|$ denotes the modulus function, then the element in the $2^{nd}$ row and $3^{rd}$ column of $A^{-1}$ is ...

If $A$ is a $3 \times 3$ matrix such that $|5 \cdot \text{adj } A| = 5$,then $|A|$ is equal to