If A is Idempotent muithen Show +hat - 3+2)":= 1+(2-1)A – InterviewSolution

1.

If A is Idempotent muithen Show +hat - 3+2)":= 1+(2-1)A

Answer»

A^2 = A

A^3, A^4, A^5.......A^n = A

(I + A)^n = nC0 I^n + nC1 I^n-1A + nC2 I^n-2 A^2 +...... nCn A^n

= nC0 I^n + nC1 A + nC2 A +...... nCn A

= 1* I + A(nC1 + nC2 +......... nCn)

= I + A[(nC0 + nC1 + nC2 +......... nCn) - nC0]

= I + (2^n - 1)A

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