Question

If $A=\left|\begin{array}{ccc}3& 2& 1\\ 4& -1& 2\\ 0& 1& 2\end{array}\right|$, then $adj\left(adjA\right)$ is

• A. $32A$
• B. $-32A$
• C. $33A$
• D. $-35A$

Answer 1

Answer: (A)

$32A$

$A=\left|\begin{array}{ccc}3& 2& 1\\ 4& -1& 2\\ 0& 1& 2\end{array}\right|=3(-2-2)-2\left(8\right)+1\left(4\right)=-12-16+4=-24$

For a matrix $A$

adj(adj$A$)$={\left|A\right|}^{n-1}A$

where $n$ is its order

$\therefore$ adj(adj $A$)$=(-24{)}^{3-1}={(-24)}^2=576A$