If A is a square matrix of order 2 × 2 and B = 1 2 3 4 , such that A B = B A , then A can be

Question

If A is a square matrix of order 2 × 2 and B = 1 2 3 4 , such that A B = B A , then A can be, 1 4 6 7, 1 4 7 6, 2 2 2 4, 3 4 4 9

MARKS App · Accepted Answer

Let, A = a b c d then a b c d 1 2 3 4 = 1 2 3 4 a b c d ⇒ a + 3 b = a + 2 c , 2 a + 4 b = b + 2 d c + 3 d = 3 a + 4 c , 2 c + 4 d = 3 b + 4 d ⇒ 3 b = 2 c , a + c = d , Hence, B = a b 3 b 2 a + 3 b 2 where a , b ∈ R Now, we see A is correct

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