JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q66

MathematicsSingle correct+4 / -1Question 66 of 90

If A is an $3\times3$ non - singular matrix such that $AA'=A'A$ and $B=A^{-1}A'$ , then $BB'$ equals :

B^{-1}

\left(B^{-1}\right)'

I+B

Answer and worked solution

Official answer: D

$BB'=A^{-1}A'\left(A^{-1}A'\right)'=A^{-1}A'A\left(A^{-1}\right)'=A^{-1}AA'\left(A'\right)^{-1}=I,$
using $A'A=AA'$ and $(A^{-1})'=(A')^{-1}$ .

JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 66