Let L V W be a linear function Suppose M, N W V are linear functions that satisfy L M I V N L Prove that M N L 1 Thus, a linear function may have only a left or a right inverse, but if it has both, then they must be the same

Question: Let L: V W be a linear function. Suppose M, N: W V are linear functions that satisfy L M = I

Let L: V → W be a linear function. Suppose M, N: W → V are linear functions that satisfy L ◦ M = I_V = N ◦ L. Prove that M = N = L⁻¹. Thus, a linear function may have only a left or a right inverse, but if it has both, then they must be the same.

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