Question

Given a square matrix $A$ of order $3\times 3$ such that $\left|A\right|=12$, find the value of | A Adj A|

Answer 1

$A=n\times n$ matrix

$|adjA|=|A{|}^{n-1}$

$|AadjA|=|A||adjA|$

$=|A||A{|}^{3-1}$

$=|A{|}^3$

$={12}^3$

$=1728$