The positive value of the determinant of the matrix A , whose...

Given,

\left[\begin{cases}14 & 28 & - 14 \\ - 14 & 14 & 28 \\ 28 & - 14 & 14\end{cases}\right] = \left(adj \left(adj A\right)\right)

Now we know that \left|adj A\right| = {A}^{2}$if it is$3 \times 3$matrix</p><p>So \left|adj \left(adj A\right)\right| = {\left|adj A\right|}^{2}$

$⇒ {\left|A\right|}^{2 \times 2} = {\left|A\right|}^{4}$

Now, {\left|A\right|}^{4} = \left|\begin{cases}14 & 28 & - 14 \\ - 14 & 14 & 28 \\ 28 & - 14 & 14\end{cases}\right|

⇒ {\left|A\right|}^{4} = {14}^{3}\left|\begin{cases}1 & 2 & - 1 \\ - 1 & 1 & 2 \\ 2 & - 1 & 1\end{cases}\right|

$⇒ {\left|A\right|}^{4} = {14}^{3} \times \left(14\right)$

${\left|A\right|}^{4} = {\left(14\right)}^{4} ⇒ \left|A\right| = 14$