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If A is an Idempotent matric and I is the idenity matrix of the same order, then the value of n such that (A +I) ​n ​ = I+27A is …...​.?

If A is an Idempotent matric and I is the idenity matrix of the same order, then the value of n such that (A +I)​n​ = I+27A is …...​.?

Grade:12

1 Answers

Vikas TU
14149 Points
7 years ago
From idpotent matrix rule that is a matrix A with when multiplying with itself would yield the matrix itself that is A matrix.
Mathematically,
A.A = A
Hence in R.H.S,
I + 27A = > I + A {multiplying A with 27 times would gve again A itself}
Therfore,
 (A +I)​n​ = I + A
Hence,
n = 1 

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