Let be a root of the equation x² + x + 1 = 0 and the
matrix A = {1 \over {\sqrt 3 }}\left[ {\matrix{
1 & 1 & 1 \cr
1 & \alpha & {{\alpha ^2}} \cr
1 & {{\alpha ^2}} & {{\alpha ^4}} \cr
} } \right]
then the matrix
A³¹ is equal to
JEE Main 2020 · 7 Jan, Morning shift · Q4500