jee-main 2020 Q59

jee-main · India · session1_07jan_shift1 Matrices Matrix Power Computation and Application

Let $\alpha$ be a root of the equation $x ^ { 2 } + x + 1 = 0$ and the matrix $A = \frac { 1 } { \sqrt { 3 } } \left[ \begin{array} { c c c } 1 & 1 & 1 \\ 1 & \alpha & \alpha ^ { 2 } \\ 1 & \alpha ^ { 2 } & \alpha ^ { 4 } \end{array} \right]$, then the matrix $A ^ { 31 }$ is equal to
(1) $A ^ { 3 }$
(2) $I _ { 3 }$
(3) $A ^ { 2 }$
(4) $A$

Let $\alpha$ be a root of the equation $x ^ { 2 } + x + 1 = 0$ and the matrix $A = \frac { 1 } { \sqrt { 3 } } \left[ \begin{array} { c c c } 1 & 1 & 1 \\ 1 & \alpha & \alpha ^ { 2 } \\ 1 & \alpha ^ { 2 } & \alpha ^ { 4 } \end{array} \right]$, then the matrix $A ^ { 31 }$ is equal to\\
(1) $A ^ { 3 }$\\
(2) $I _ { 3 }$\\
(3) $A ^ { 2 }$\\
(4) $A$

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