Find the inverse of a 2x2 matrix

Consider the 2x2 matrix M, consisting of elements a, b, c and d. To find its inverse one must first find the determinant of M. This is achieved by calculating the result of the expression ad - bc. The inverse of M is subsequently found by multiplying the reciprocal of the determinant (1/ad - bc) by a rearrangement of the original matrix such that the positions of a and d are swapped and b and c are multiplied by -1. For the inverse to exist the determinant of M must be non-zero, since the reciprocal of zero is infinite. This suggests that for some matrices there exists no inverse and so these and referred to as singular.