Question

# If a $$n\times n$$ square matrix $$A$$ is such that $$\left| A \right| =D$$ and $$\left| adj\quad A \right| =D'$$, then-

A
DD=Dn
B
DD=Dn1
C
DD=D2
D
none of these

Solution

## The correct option is B $$DD'={D}^{n}$$Considering that $$A$$ is an nth order square matrix, then$$|adjA|=|A|^{n-1}$$Now it is given that $$|adjA|=D'$$ and $$|A|=D$$.Hence $$D'=D^{n-1}$$Or $$D'=\dfrac{D^{n}}{D}$$Or $$D.D'=D^{n}$$Applied Mathematics

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