Question: 3. (a) Show that for all idempotent matrices B that either |B| = 1 or B is singular. (b) Consider the matrix A= [a b]

3. (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

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