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If A is an idempotent matrix, then show ...

If A is an idempotent matrix, then show that B=l-A is also idempotent and AB=BA=0

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To show that if \( A \) is an idempotent matrix, then \( B = I - A \) is also idempotent and that \( AB = BA = 0 \), we can follow these steps: ### Step 1: Definition of Idempotent Matrix An idempotent matrix \( A \) satisfies the property: \[ A^2 = A \] ...
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