Question

Let $A=[a_{ij}{]}_{n\times n}$ be a square matirx and let $c_{ij}$ be cofactor of $a_{ij}$ in A. If $C=\left[c_{ij}\right]$, then

• A. $|C|=|A|$
• B. $|C|=|A{|}^{n-1}$
• C. $|C|=|A{|}^{n-2}$
• D. none of these

Answer 1

Answer: (B)

$|C|=|A{|}^{n-1}$

$C\to$ Cofactor matrix

$AdjA={\left(C\right)}^{{}^T}$

But det of $AdjA=DetofC$

Because they are transpore of each other .

$\Rightarrow \left|AdjA\right|=\left|C\right|={\left|A\right|}^{n-1}$

Option-B