Assertion (A): If $B$ is a $3 \times 3$ matrix and $|B|=6$, then $|\operatorname{Adj}(B)|=36$ Reason (R): If…

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 $|\operatorname{Adj}(B)|=|B|^{\mathbf{n}}$
  1. Both (A) and (R) are true and (R) is the correct explanation of (A)
  2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
  3. (A) is true but (R) is false
  4. (A) is false but (R) is true

Solution

$|B|=6 \Rightarrow|\operatorname{Adj}(B)|=6^{3-1}=36$ Since $\left|B_{n \times n}\right|=k \Rightarrow|\operatorname{Adj}(B)|=k^{\mathrm{n}-1}$.

Asked in: AP EAMCET 2024 (21 May Shift 2)

Practice more Matrices questions on Aicharya