56. Let V be an *n* *n* symmetric positive definite matrix such that V = P'P,...

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56. Let V be an *n* × *n* symmetric positive definite matrix such that V = P'P, where P has size *n* × *n*, and let A be a symmetric *n* × *n* matrix. Show that PAP is a symmetric idempotent matrix if and only if AV is an idempotent matrix.

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