If $\left|A\right|=100$, find $\left|A^{-1}\right|$.

$\left(\begin{array}{cc}2& 9\\ -3& 1\end{array}\right)$

Use elementary row operation to determine whether the following matrix is invertible and hence find the inverse whenever possible.

$\left(\begin{array}{ll}e& \pi \\ \pi & e\end{array}\right)$

$\left(\begin{array}{ccc}1& 2& 1\\ 2& 1& -1\\ 1& 5& 4\end{array}\right)$

$\left(\begin{array}{lll}1& 2& 1\\ 1& 0& 1\\ 1& 1& 1\end{array}\right)$

$\left(\begin{array}{ccc}1& 2& 1\\ -1& 1& 2\\ 1& 0& 1\end{array}\right)$

$\left(\begin{array}{ccc}1& 2& 1\\ 1& 3& 4\\ 2& 3& -1\end{array}\right)$

Find the inverse of the following matrix using elementary column operations.

$\left(\begin{array}{cc}2& 9\\ -3& 1\end{array}\right)$