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Determinants — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDeterminants1 Mark
Question
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.
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Answer

(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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