Mathematics | VITEEE 2016 | Discussion Page

If A and B are matrices and B= ABA^-1 then the value of (A+B) (A-B) is

$A^{2}+B^{2}$

$A^{2}-B^{2}$

C) A+B

D) A-B

Option B

B= ABA^-1(Given)

But B= BAA^-A

$\therefore$ $ABA^{-1}=BAA^{-1}\Rightarrow AB=BA$

Now $(A+B)(A-B)=A^{2}-AB+BA-B^{2}$

$A^{2}-AB+BA-B^{2}[\because AB=BA]$

= $A^{2}-B^{2}$

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