Suppose T U V and S V W are linear transformations and dim (U) dim (V) dim (W) Suppose that S T is invertible Prove that S and T are individually invertible (this could be construed as a converse of Theorem CIVLT)

Question: Suppose T: U V and S: V W are linear transformations and dim (U) = dim (V) = dim (W). Suppose that S

Suppose T: U → V and S: V → W are linear transformations and dim (U) = dim (V) = dim (W). Suppose that S ο T is invertible. Prove that S and T are individually invertible (this could be construed as a converse of Theorem CIVLT).

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