The value of $\begin{bmatrix}5^2 & 5^3 & 5^4\\5^3 & 5^4 & 5^5\\5^4 & 5^5 & 55^6\end{bmatrix}, $ is

0

The correct answer is option (2) : 0

Let,

$Δ=\begin{bmatrix}5^2 & 5^3 & 5^4\\5^3 & 5^4 & 5^5\\5^4 & 5^5 & 55^6\end{bmatrix}$

$⇒Δ=5^2×5^3v5^4\begin{bmatrix}1 & 5 & 5^2\\1 & 5 & 5^2\\1 & 5 & 5^2\end{bmatrix}$            $\begin{bmatrix}taking\,  5^2, 5^3 \, and\,  5^4\\common\,  from\,  R_1, R_2\\and\,  R_3 \, respectively\end{bmatrix}$

$⇒Δ=5^9×5×5^2\begin{bmatrix}1 & 1 & 1\\1 & 5 & 5^2\\1 & 5 & 5^2\end{bmatrix}$                    $\begin{bmatrix}Taking \, 5 \, and \, 5^2\,  common\\from \, C_2 \, and \, C_3 \, respectively\end{bmatrix}$

$⇒Δ=5^{12}×0 = 0 $