How to convert a permutation group into linear transformation matrix? is there any example about apply isomorphism to permutation group
and how to convert linear transformation matrix to permutation group and convert back to linear transformation matrix

Hint:Prove that Permutatation matrices form a subgroup of $\mathbb{GL}_n(R)$(under multiplication) and this subgroup is isomorphic to $S_n$.
You can visualize it if you think of the way permutation matrices work when they are applied from the left to any matrix. 
Permutation matrices just change the positions of some rows when they are applied from the left to some matrix.
Multiplying two permutation matrix results in another permutation matrix because In a matrix if we apply two permutation matrices from the left we are left with another matrix haing the same rows but in a different position so it can again be represented by another permutation matrix.
Clearly the permutation matrix doing the reverse change of these rows will be its inverse.
The homomorphism that shows the two groups to be isomorphic is $\phi(P)=(\sigma_1,\sigma_2,\dots ,\sigma_n)$. Here $\sigma_i $ is the row number where the $i$ th row of any matrix go when $P$ is applied to it from the left.
