Question: Prove that if L: U U is an invertible linear transformation on an inner product space U, then the following three statements are equivalent:

Prove that if L: U → U is an invertible linear transformation on an inner product space U, then the following three statements are equivalent:
(a) (L[u], L[v]) = (u, v) for all u, v ∈ U
(b) ||L[u]|| = ||u|| for all u ∈ U
(c) L* = L-1.

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