Question

If $A=\left[\begin{array}{ccc}2& -1& 3\\ -5& 3& 1\\ -3& 2& 3\end{array}\right]$, then $A.\left(AdjA\right)=$

• A. $\left(Adj{.A}^T\right)$
• B. $(Adj.A).A$
• C. $|A|.A$.
• D. None of these

Answer 1

The correct option is B $(Adj.A).A$

$A^{-1}=\frac{adjA}{|A|}$

${AA}^{-1}=\frac{A\left(adjA\right)}{|A|}$

$\therefore A\left(AdjA\right)=|A|I$

Also $\left(AdjA\right)A=A\left(AdjA\right)=|A|I$

Option B satisfies