Question: (a) Prove that if Q is an orthogonal matrix, then ||Qx|| = ||x|| for any vector x Rn, where |||| denotes the standard Euclidean

(a) Prove that if Q is an orthogonal matrix, then ||Qx|| = ||x|| for any vector x ∊ Rn, where ||∙|| denotes the standard Euclidean norm.
(b) Prove the converse: if ||(Qx|| = ||x|| for all x ∊ Rn, then Q is an orthogonal matrix.

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