Consider A = a 11 a 12 a 21 a 22 and B = 1 1 2 1 such that A B = B A , then the value of a 12 a 21 + a 11 a 22 is

Question

Consider A = a 11 a 12 a 21 a 22 and B = 1 1 2 1 such that A B = B A , then the value of a 12 a 21 + a 11 a 22 is, 2, 4, 3 2, 1 2

MARKS App · Accepted Answer

Given: A B = B A a 11 a 12 a 21 a 22 1 1 2 1 = 1 1 2 1 a 11 a 12 a 21 a 22 a 11 + 2 a 12 a 11 + a 12 a 21 + 2 a 22 a 21 + a 22 = a 11 + a 21 a 12 + a 22 2 a 11 + a 21 2 a 12 + a 22 a 11 + 2 a 12 = a 11 + a 21 ⇒ 2 a 12 = a 21 a 11 + a 12 = a 12 + a 22 ⇒ a 11 = a 22 a 21 + 2 a 22 = 2 a 11 + a 21 ⇒ a 11 = a 22 a 21 + a 22 = 2 a 12 + a 22 ⇒ a 21 = 2 a 12 a 12 a 21 = 1 2 , a 11 a 22 = 1

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