Question

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

A
|C|=|A|
B
|C|=|A|n1
C
|C|=|A|n2
D
none of these

Solution

## The correct option is D $$|C|=|A|^{n-1}$$$$C\rightarrow$$ Cofactor matrix $$AdjA= \left (C \right )^{^{T}}$$But det of $$AdjA= Det \quad of \quad C$$Because they are transpore of each other .$$\Rightarrow\left | AdjA \right | = \left | C \right |= \left | A \right |^{n-1}$$Option-BMathematics

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