$A$ and $B$ are $n$-rowed square matrices such that $AB = O$ and $B$ is non-singular. Then:

Let the matrix $A = \begin{bmatrix} 10^{30} + 5 & 10^{20} + 4 & 10^{20} + 6 \\ 10^4 + 2 & 10^8 + 7 & 10^{10} + 2n \\ 10^4 + 8 & 10^6 + 4 & 10^{15} + 9 \end{bmatrix}$,where $n \in N$. Then:

If $A = \begin{bmatrix} 1 & \cot \frac{\theta}{2} \\ -\cot \frac{\theta}{2} & 1 \end{bmatrix}$,then $A^{-1} =$

Using elementary transformations,find the inverse of the following matrix,if it exists: $\left[\begin{array}{cc}7 & 4 \\ 1 & -2\end{array}\right]$

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

Find the inverse matrix of $\begin{bmatrix} 4 & 7 \\ 1 & 2 \end{bmatrix}$.