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

If A is idempotent matrix, then show that
`(A+I)^(n) = I+(2^(n)-1) A, AAn in N,` where I is the identity
matrix having the same order of A.

Text Solution

AI Generated Solution

To prove that if \( A \) is an idempotent matrix, then \[ (A + I)^n = I + (2^n - 1) A, \] where \( I \) is the identity matrix of the same order as \( A \), we will follow these steps: ...
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