3. Let V be a finite dimensional vector space and let (.,.,) be an inner product on V. Suppose that V ‡ {0}. Define || · ||: V → [0, ∞) by ||u|| = √√(u, u). So || · || is the norm associated with the inner product. Let T: V → V be a linear map. Suppose that ||Tu|| = ||u|| for all u € V. Prove that T is orthogonal.

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A: According to our guidelines we can answer only one question and rest can be reposted.

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