# Let 1 2 3 4 A æ ö = ç ÷ è ø and 0 0 a B b æ ö = ç ÷ è ø, ab N , Î . Then

Question:

Let $A=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right)$ and $B=\left(\begin{array}{cc}a & 0 \\ 0 & b\end{array}\right), a, b \in N$. Then

1. there cannot exist any $\mathrm{B}$ such that $\mathrm{AB}=\mathrm{BA}$

2. there exist more than one but finite number of $B^{\prime} s$ such that $\mathrm{AB}=\mathrm{BA}$

3. there exists exactly one $\mathrm{B}$ such that $\mathrm{AB}=\mathrm{BA}$

4. there exist infinitely many $\mathrm{B}^{\prime}$ s such that $\mathrm{AB}=\mathrm{BA}$

Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year 2004

Solution:

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