If A is a non-null diagonal matrix of order 3 such that A 4 = A 2 , then the possible number of matrices A are

Question

If A is a non-null diagonal matrix of order 3 such that A 4 = A 2 , then the possible number of matrices A are, 27, 26, 8, 7

MARKS App · Accepted Answer

Let, A = d 1 0 0 0 d 2 0 0 0 d 3 A 2 = d 1 2 0 0 0 d 2 2 0 0 0 d 3 2 & A 4 = d 1 4 0 0 0 d 2 4 0 0 0 d 3 4 ∵ A 4 = A 2 ⇒ d 1 4 = d 1 2 ⇒ d 1 = 0,1 , - 1 d 2 4 = d 2 2 ⇒ d 2 = 0,1 , - 1 d 3 4 = d 3 2 ⇒ d 3 = 0,1 , - 1 ∵ A can't be a null matrix so the total number of possible matrices is = 3 3 - 1 = 26

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