Question: 6. Let A be a square matrix of order n. Given that Au and Av are orthogonal for any pair of orthogonal vectors u

6. Let A be a square matrix of order n. Given that

6. Let A be a square matrix of order n. Given that Au and Av are orthogonal for any pair of orthogonal vectors u and v in R". Prove that A = cP, where c E R and P is an orthogonal matrix. [Hint: Consider the standard basis {e1,...,en} for R".] [5]

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