Question

2x2 matrix with no inverse

Answer 1

Well, for a 2x2 Matrix the Inverse is:

Answer 2

The Inverse of A is A-1 only when A × A-1 = A-1 × A = I.
To find the Inverse of a 2x2 Matrix: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc).
Sometimes there is no Inverse at all.