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Let alpha be a root of the equat...

Let ` alpha ` be a root of the equation ` x ^(2) + x + 1 = 0 ` and the matrix ` A = ( 1 ) /(sqrt3) [{:( 1,,1,,1),( 1,, alpha ,, alpha ^(2)), ( 1 ,, alpha ^(2),, alpha ^(4)):}] `
then the matrix ` A ^( 31 ) ` is equal to :

A

A

B

`A^(2)`

C

`A^(3)`

D

`I_(3)`

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The correct Answer is:
C
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