Question: Suppose that T1 : Rn Rm and T2 : Rm Rp are linear transformations. (a) If T1 and T2 are injective, prove that T2 T1

Suppose that T1 : Rn Rm and T2 : Rm Rp are linear transformations.

(a) If T1 and T2 are injective, prove that T2 T1 is injective.

(b) If T1 and T2 are surjective, prove that T2 T1 is surjective.

(c) If T1 and T2 are invertible, prove that T2 T1 is invertible.

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