Question

Given a square matrix $A$ of order $3\times 3$ such that $\mid A\mid =12$, find the value of $|AadjA|$

Answer 1

Compute the required value.

Given: Matrix $A$ of order $3\times 3$ and $\mid A\mid =12$

Since, $\left|adjA\right|={\left|A\right|}^{n-1}$

$\begin{array}{rcl}|AadjA|& =& \left|A\right|\left|adjA\right|\\ & =& \left|A\right|{\left|A\right|}^{3-1}\\ & =& {\left|A\right|}^3\\ & =& {\left(12\right)}^3\\ & =& 1728\end{array}$

Hence, the value of $|AadjA|$ is $1728$.