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If A and B are n-rowed unitary matrices,...

If A and B are n-rowed unitary matrices,then AB and BA are also unitary matrices.

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To prove that if \( A \) and \( B \) are \( n \)-rowed unitary matrices, then \( AB \) and \( BA \) are also unitary matrices, we will follow these steps: ### Step 1: Definition of Unitary Matrices A matrix \( U \) is called unitary if \( U^* U = I \), where \( U^* \) is the conjugate transpose of \( U \) and \( I \) is the identity matrix. ### Step 2: Given Information We know that \( A \) and \( B \) are unitary matrices. Therefore, we have: \[ ...
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