If d is the determinant of a square matrix A | vedclass

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(B) We know that for any square matrix $A$ of order $n$,the relationship between the matrix and its adjoint is given by $A(	ext{adj } A) = |A| I_n$,w

Vedclass · Accepted Answer

$d^{n-1}$

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(B) We know that for any square matrix $A$ of order $n$,the relationship between the matrix and its adjoint is given by $A(	ext{adj } A) = |A| I_n$,where $I_n$ is the identity matrix of order $n$.Taking the determinant on both sides,we get $|A(	ext{adj } A)| = ||A| I_n|$.Using the property $|AB| = |A||B|$,we have $|A| |	ext{adj } A| = |A|^n |I_n|$.Since $|I_n| = 1$,this simplifies to $|A| |	ext{adj } A| = |A|^n$.Given that $|A| = d$,we have $d |	ext{adj } A| = d^n$.Therefore,$|	ext{adj } A| = d^{n-1}$.

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

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