Let 5: Rn Rn and T: Rn Rn be linear transformations with matrices A and

Question:

Let 5: Rn → Rn and T: Rn → Rn be linear transformations with matrices A and B respectively. [Theorem 3.]
(a) Show that B2 = B if and only if T2 = 7 (where T2 means T o T).
(b) Show that B2 = 1 if and only if T2 = 1Rn.
(c) Show that AB = BA if and only if S o T = T o S.