Let A = 1 & 2 \\ 3 & 4 and B = a & 0 \\ 0 & b , a, b N . Then: - Mathematics MCQ AIEEE 2006 2026 | ExamTest.live

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Let A = (1324) and B = (a 0 0 b), a, b \in N . Then:

Solution & Step-by-step Explanation

A B = (1324) (a 0 0 b) = (a 3 a 2 b 4 b) B A = (a 0 0 b) (1324) = (a 3 b 2 a 4 b) For A B = B A : a = a 2 b = 2 a ⟹ a = b 3 a = 3 b ⟹ a = b 4 b = 4 b So A B = B A if and only if a = b .Since a, b \in N, there are infinitely many pairs (a, a) that satisfy this.

Try it yourself before checking the explanation above.

Let A = (1324) and B = (a 0 0 b), a, b \in N . Then:

there cannot exist any B such that A B = B A

there exist more than one but finite number of B's such that A B = B A

there exists exactly one B such that A B = B A

there exist infinitely many B's such that A B = B A

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