Question

If A is a matrix of order 3 and |A| = 8, then |Adj A| =

• A. $1$
• B. $2$
• C. $2^3$
• D. $2^6$

Answer 1

The correct option is D $2^6$

We know $A.adj\left(A\right)=\left[\begin{array}{ccc}|A|& 0& 0\\ 0& |A|& 0\\ 0& 0& |A|\end{array}\right]\therefore |A|.|adj\left(A\right)|=\left|\begin{array}{ccc}|A|& 0& 0\\ 0& |A|& 0\\ 0& 0& |A|\end{array}\right|\therefore |A|.|adjA|=|A{|}^3$
Now question gives |A| = 8
$\therefore 8.|adjA|=8^3$ or $|adjA|=8^2=(2^3{)}^2=2^6$.