Tricky Matrix

Algebra Level 2

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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