question_answer

Let \[\alpha \] be a root of the equation \[{{x}^{2}}+x+1=0\] and the matrix  then matrix \[{{A}^{31}}\] is equal to: [JEE MAIN Held on 07-01-2020 Morning]

A) \[{{A}^{2}}\]      

B)   A         

C) \[{{I}_{3}}\]               

D) \[{{A}^{3}}\]

Correct Answer: D

Solution :

[d] \[\alpha =\omega \text{ }or\,{{\omega }^{2}}\] \[\Rightarrow {{A}^{31}}={{A}^{3}}\]