1) If A and B are matrices and B= ABA-1 then the value of (A+B) (A-B) is A) $A^{2}+B^{2}$ B) $A^{2}-B^{2}$ C) A+B D) A-B Answer: Option BExplanation: B= ABA-1(Given) But B= BAA-A $\therefore$ $ABA^{-1}=BAA^{-1}\Rightarrow AB=BA$ Now $(A+B)(A-B)=A^{2}-AB+BA-B^{2}$ $A^{2}-AB+BA-B^{2}[\because AB=BA]$ = $A^{2}-B^{2}$
