if A is a square matrix of order 3 such that modulus A = 5 then write the value of A (adj A)

In the given question, we are given a square matrix of order 3 such that $\left|A\right|=5$. We need to find $\left|A.adjA\right|$.

Here, use the formula $A^{-1}=\frac{adjA}{\left|A\right|}$. So,
$A^{-1}.\left|A\right|=adjA$

Next, multiply left hand side and right hand side by A, we get
$A.A^{-1}.\left|A\right|=A.adjA$

No, use the fact that $A.A^{-1}=I_3$ where I₃ is the identity matrix of order 3. So,
$$\begin{gathered} \left|A\right|.I_3=A.adjA \\ \left|\left|A\right|.I_3\right|=\left|A.adjA\right| \\ {\left|A\right|}^3=\left|A.adjA\right| \\ {5}^3=\left|A.adjA\right| \\ \left|A.adjA\right|=125 \end{gathered}$$

Therefore, $\left|\mathbf{A}\mathbf{.}\mathbf{a}\mathbf{d}\mathbf{j}\mathbf{A}\right|\mathbf{=}\mathbf{125}$