Without expanding the determinants, show that [(xa, yb, zc) (a^2 , b^2, c^2) (1, 1, 1)] = [(x, y, z) (a, b, c) (bc, ca, ab)]

Question

Without expanding the determinants, show that

\(\begin{vmatrix}xa&yb&zc\\a^2&b^2&c^2\\1&1&1\end{vmatrix} = \begin{vmatrix}x&y&z\\a&b&c\\bc&ca&ab\end{vmatrix}\)

[(xa, yb, zc) (a² , b², c²) (1, 1, 1)] = [(x, y, z) (a, b, c) (bc, ca, ab)]

Answer 1

L.H.S. = \(\begin{vmatrix}xa&yb&zc\\a^2&b^2&c^2\\1&1&1\end{vmatrix}\)