3. Suppose A, B E M2x2(Z) and n E N. We say A = B mod n if the individual entries in A and B are congruent modulo n, i.e. aij = bij mod n for 1 Z. d) We say that [A] E M2x2(Z) is invertible if there is a matrix [B] E M2x2(Z) with [A][B] = [/]. Show that [ A] is invertible if and only if det[ A] is invertible in Z. e) Let G = GL2(Z) be the set of invertible elements of M2x2(Z). Show that G is a group, where the binary operation on G is given by matrix multiplication. f) How many elements does GL2(Z/2) have? Write down representatives of each element. g) By considering the action of M2x2(Z/2) on two-dimensional "vectors" with entries in Z/2, show that GL2(Z/2) can be identified with the symmetric group S3