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If A is square matrix such that `A^(2)=A`, then show that `(I+A)^(3)=7A+I`.

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To solve the problem, we need to show that if \( A \) is a square matrix such that \( A^2 = A \), then \( (I + A)^3 = 7A + I \). ### Step-by-step Solution: 1. **Understanding the Given Condition**: We know that \( A^2 = A \). This indicates that \( A \) is an idempotent matrix. 2. **Using the Binomial Expansion**: ...
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