Let α be a root of the equation x² + x + 1 = 0 and the matrix A = 1/(3)[ 1 1 1 1 α α ² 1 α ² α ⁴ ] then the matrix A³¹ is equal to

Matrices and Determinants: JEE Main 2020 Mathematics question

JEE Main 2020 · 7 Jan, Morning shift · Q4500

JEE Main 20207 Jan, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

\alpha

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

JEE Main 20207 Jan, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

\alpha

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