If P = a b c b c a c a b , a b c = 1 , P T P = I then the value of a 3 + b 3 + c 3 is

Question

If P = a b c b c a c a b , a b c = 1 , P T P = I then the value of a 3 + b 3 + c 3 is, 2, 1, 0, 5

MARKS App · Accepted Answer

Given, P = a b c b c a c a b ∴ P T = a b c b c a c a b Also given P T P = I ∴ P T P = I = 1 or a b c b c a c a b 2 = 1 ⇒ a b c b c a c a b = ± 1 or 3 a b c - a 3 - b 3 - c 3 = ± 1 or 3 ∓ 1 = a 3 + b 3 + c 3 ∴ a 3 + b 3 + c 3 = 2 or 4

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