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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
Assertion (A) : If $A=\left(\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right)$, then $\operatorname{adj}(\operatorname{adj} A)=A$.
Reason (R) : $|\operatorname{adj}(\operatorname{adj} A)|=|A|^{(n-1)^2}, A$ be $n$ rowed non singular matrix.
  • A
    Both (A) and (R) are true and (R) is the correct explanation of (A).
  • ✓
    Both (A) and (R) are true but (R) is not the correct explanation of (A).
  • C
    (A) is true but (R) is false.
  • D
    (A) is false but (R) is true.
✓

Answer

Correct option: B.
Both (A) and (R) are true but (R) is not the correct explanation of (A).
(b): $\operatorname{adj}(\operatorname{adj} A)=|A|^{n-2} A$
Here, $n=3$
$\therefore \quad \operatorname{adj}(\operatorname{adj} A)=|A| A$ ....(i)
Now, $|A|=\left|\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right|=3(-3+4)+3(2)+4(-2)=1$
From Eq. (i), adj $(\operatorname{adj} A)=A$

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