Q44 / 160 · AP EAMCET 2022 (08 Jul Shift 1) · Mathematics

If $A=\left[\begin{array}{ccc}1 & -3 & 2 \\ -2 & 1 & 3 \\ 3 & 2 & -1\end{array}\right]$ then $A^2 \operatorname{Adj} A=$

  • A
    $21 \mathrm{~A}$
  • Correct answer
    B
    $-42 \mathrm{~A}$
  • C
    $7 \mathrm{~A}-1$
  • D
    $14(\operatorname{Adj} A)$

Solution

$|\mathrm{A}|\left|\begin{array}{ccc}1 & -3 & 2 \\ -2 & 1 & 3 \\ 3 & 2 & -1\end{array}\right|$ $\begin{aligned} & =1-(-1-6)+3(2-9)+2(-4-3) \\ & =-7-21-14=-42\end{aligned}$ Now, $A^2 \operatorname{adj} A=A \cdot A \operatorname{adj} A=A|A|=-42$

Hence, the correct answer is option: 'B'.

Relevant Questions