Hello.

A Matrix B is non-singular if

So in this case the determinant of your matrix is 1, that means it is non-singular.

I usually find inverse using Gauss method.

First to make we do the transformation

after doing that transformation it will be

now a12 should be 0. So we do the transformation

you'll have

now you divide the first row by and the second row with

and you'll have:

So the inverse of that matrix is

You can check your results by multyplying if the result is the Identity matrix , then it's done well.