Find the inverse of the general 2x2 matrix A= ([a, b],[c, d]) when does this inverse exist?

This is a typical further maths question, doing it correctly is a matter of carrying out a two-step process. 

Start by finding the determinant of the matrix,

det(A)=ad-bc

Then swap the entries a d and negate the other entries. After dividing by the determinant the inverse of A is given.

A^-1=1/(ad-bc)([d -b],[-c, a]).