Question: Prove that A is normal if and only if the Hermitian and skew-Hermitian matrices in Prob. 18 commute. Data from Prob. 18 This important concept

Prove that A is normal if and only if the Hermitian and skew-Hermitian matrices in Prob. 18 commute.

Data from Prob. 18

This important concept denotes a matrix that commutes with its conjugate transpose, AA̅^T = A̅^TA. Prove that Hermitian, skew-Hermitian, and unitary matrices are normal. Give corresponding examples of your own.

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