Q46 / 160 · AP EAMCET 2024 (21 May Shift 2) · Mathematics
Assertion (A): If $B$ is a $3 \times 3$ matrix and $|B|=6$, then $|\operatorname{Adj}(B)|=36$
Reason (R): If $B$ is a square matrix of order $n$, then $|\operatorname{Adj}(B)|=|B|^{\mathbf{n}}$
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- Correct answerC(A) is true but (R) is false
- D(A) is false but (R) is true
Solution
$|B|=6 \Rightarrow|\operatorname{Adj}(B)|=6^{3-1}=36$
Since $\left|B_{n \times n}\right|=k \Rightarrow|\operatorname{Adj}(B)|=k^{\mathrm{n}-1}$.
Hence, the correct answer is option: 'C'.