Question

9.
If A is 3x3 non-singular matrix then
det (A-'adja)=
A) det A B) 1 C) (det A) D) (det A)"​

Answer 1

$\text{I think that your question is:}$

$\text{If A is 3{\times}3 non-singular matrix then}\;det(A'\,adjA)$

$\textbf{Given:}$

$\text{A is a 3{\times}3 non singular matrix}$

$\textbf{To find:}$

$det(A'\,adjA)$

$\textbf{Solution:}$

$\text{We know that,}$

$\textbf{If A and B are two matrices of same order n, then}$

$\bf\,det(AB)=det(A)\,det(B)$

$\bf\,det(A')=det(A)$

$\bf\,det(adjA)=[det(A)]^{n-1}$

$\text{Consider,}$

$det(A'\,adjA)$

$=det(A')\,det(adjA)$

$=det(A)\,det(adjA)$

$=det(A)\,[det(A)]^2$

$=[det(A)]^3$

$\textbf{Answer:}$

$\bf\,det(A'\,adjA)=[det(A)]^3$