here we need to see the inverse of a matrix

Question

Here we need to see the inverse of a matrix. Provided a square matrix, A, of size n x n if we can get the other matrix of similar size, B that,

AB = BA = I_n after that we call B the inverse of A and denote it by B=A^-1.

Calculating the inverse of a matrix, A, is quite simple. Firstly we form a new matrix,

(A I_n)

And after that use the row operations from the earlier section and try to change this matrix in the form,

(I_n B)

If we can so B is the inverse of A.  If we can't so there is no inverse of the matrix A.