# If A and B are square matrices of sie n × n such that 2 2 A B ABAB – =- + ( )( ) , then which of the following will be always true?

Question:

If $A$ and $B$ are square matrices of size $n \times n$ such that $A^{2}-B^{2}=(A-B)(A+B)$, then which of the following will be always true?

1. $A=B$

2. $A B=B A$

3. either of $A$ or $B$ is a zero matrix

4. either of $A$ or $B$ is identity matrix

Correct Option: 2

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year 2006

Solution:

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