Let $A = [a_{ij}]$ be a square matrix of order 3 with $|A|= 2$ and let $C = [C_{ij}]$, where $C_{ij}$ = cofactor of $a_{ij}$ in A. Then $|C|$ is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
Given:
$|A| = 2$, and $C = [C_{ij}]$ is the cofactor matrix of $A$.
Property:
For a square matrix of order $n$,
$|\text{adj}(A)| = |C| = |A|^{n-1}$
For $n = 3$:
$|C| = |A|^{3-1} = |A|^2$
Substitute $|A| = 2$:
$|C| = 2^2 = 4$
Therefore, $|C| = 4$.