Consider a matrix
\(A= \begin{bmatrix}
l & m & n \\
p & q & r \\
1 & 1 & 1
\end{bmatrix}\). If \( (l-m)^{2}+(p-q)^{2}=9\), \( (m-n)^{2}+(q-r)^{2}=16\) and \((n-l)^{2}+(r-p)^{2}=25\).
Find \(\det (B)\), if \(B=A^{2}\)

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