Show that |(1,a,a),(a,1,a),(a,a,1)|^2 = |(1 - 2a^2,-a^2,-a^2),(-a^2,-1,a^2 - 2a),(-a^2,a^2 - 2a,-1)|

Question

Show that \(\begin{vmatrix} 1 &a&a \\[0.3em]a&1&a\\a&a&1\end{vmatrix}^2\)=  \(\begin{vmatrix} 1 - 2a^2&-a^2&-a^2 \\[0.3em]-a^2&-1&a^2 - 2a\\-a^2&a^2 - 2a&-1\end{vmatrix}\)

Answer 1

LHS = \(\begin{vmatrix} 1 &a&a \\[0.3em]a&1&a\\a&a&1\end{vmatrix}^2\)