Using die property of determinants and without prove the follow.
\(\begin{vmatrix}
b + c &q + r & y + z \\[0.3em]
c + a& r + p &z + x\\[0.3em]
a + b & p + q& x + y
\end{vmatrix}\) = 2\(\begin{bmatrix}
a& p& x \\[0.3em]
b & q &y \\[0.3em]
c & r&z
\end{bmatrix}\)
