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
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.