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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
$A =\left[\begin{array}{ll}0 & 3 \\ 2 & 0\end{array}\right]$ and $A ^{-1}=\lambda(\operatorname{adj}( A ))$, then $\lambda=$
  • ✓
    $\frac{-1}{6}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{-1}{3}$
  • D
    $\frac{1}{6}$
✓

Answer

Correct option: A.
$\frac{-1}{6}$
(A) $| A |=\left|\begin{array}{ll}0 & 3 \\ 2 & 0\end{array}\right|=-6 \neq 0$
$A ^{-1}=\frac{1}{|A|} \operatorname{adjA}$
$=\lambda(\operatorname{adj} A )$ ....[Given]
$\therefore \quad \lambda=\frac{1}{|A|}=-\frac{1}{6}$

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