If A is a square matrix of order 3, then adj A is equal to:

$|A|$ $|A|^2$ $|A|^3$ $3|A|$

$|A|^2$

$A\,adj\, A=|A|I_{3×3}$ So appearing determinant on both side we get, $|A\,adj\, A|=|A|^3$ $=|A||adj\, A|=|A|^3$ $⇒|adj\, A|=|A|^2$