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

Mathematics

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