Question

If $\left|\right(adjA\left)\right|=81,$ for $3\times 3$ matrix, then det $A$ is equal to

• A. $1$
• B. $2$
• C. $4$
• D. $9$

Answer 1

The correct option is D $9$

Given for a square matrix $A$ of order $3$.

$|adjA|=|A{|}^{n-1}$, where $n$ is the order of matrix.

We have, $|adj\left(A\right)|=|A{|}^{(3-1)}$

or, $|A{|}^2=81$

or, $|A|=9$. [ Taking the positive value]