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Let A= ( … ) and B= ( … ), a, b ∈ N. Then

JEE Main 2006 — Mathematics Algebra

2006mcqmedium

Let A=(1234)A=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right)A=(13​24​) and B=(a00b),a,b∈NB=\left(\begin{array}{ll}a & 0 \\ 0 & b\end{array}\right), a, b \in NB=(a0​0b​),a,b∈N. Then

Official previous-year question

Held on 30 Apr 2006 · Verified 6 Jul 2026.

Options

  1. A

    there cannot exist any B such that AB = BA

  2. B

    there exist more than one but finite number of B’s such that AB = BA

  3. C

    there exists exactly one B such that AB = BA

  4. D

    there exist infinitely many B’s such that AB = BA

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