A show that for all idempotent matrices b that either b 1

Question

(a) Show that for all idempotent matrices B that either |B| = 1 or B is singular.

(b) Consider the matrix A= [a b]

b a

where a and b are constants. Find all pairs (a, b) such that A is idempotent.

(c) For each pair (a, b) obtained in (b) determine whether A falls into the category of |A| = 1 or A being singular