Tricky Matrix

Level pending

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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