If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is
Question:

If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is

(a) $d^{n}$

(b) $d^{n-1}$

(c) $d^{n+1}$

 

(d) $d$

Solution:

(b) $d^{n-1}$

We know,

$|\operatorname{adj} A|=|A|^{n-1}$

$\Rightarrow|\operatorname{adj} A|=d^{n-1}$

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