Find the inverse of the following matrices, if they exist, by using elementary operations.

$\left[\begin{array}{cc}10& -2\\ -5& 1\end{array}\right]$

Find the inverse of the following  matrices, if they exist, by using elementary operations.

$\left[\begin{array}{ccc}3& 0& -1\\ 2& 3& 0\\ 0& 4& 1\end{array}\right]$

Find the inverse of the following  matrices, if they exist, by using elementary operations.

$\left[\begin{array}{ccc}1& 2& 3\\ 2& 5& 7\\ -2& -4& -5\end{array}\right]$

Find the inverse of the following  matrices, if they exist, by using elementary operations.

$\left[\begin{array}{ccc}2& -1& 4\\ 4& 0& 2\\ 3& -2& 7\end{array}\right]$

Using elementary row operations, find the inverse of the following matrix :

$\mathrm{A}=\left[\begin{array}{ccc}2& -1& 3\\ -5& 3& 1\\ -3& 2& 3\end{array}\right]$

Construct a $(2\times 2)$ matrix $\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right]$, elements of which are given by:

${\mathrm{a}}_{\mathrm{ij}}=\left\{\begin{array}{l}\mathrm{i}-\mathrm{j} \mathrm{if} \mathrm{i}\ge \mathrm{j}\\ \mathrm{i}+\mathrm{j} \mathrm{if} \mathrm{i}<\mathrm{j}\end{array}\right.$

Construct a $(2\times 3)$ matrix $\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right]$, the elements ${\mathrm{a}}_{\mathrm{ij}}$ of which are given by ${\mathrm{a}}_{\mathrm{ij}}=\left[\frac{\mathrm{i}}{\mathrm{j}}\right]$, where $\left[x\right]$ denotes the greatest integer function.