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Let alpha be a root of the equation x ^(...

Let `alpha` be a root of the equation `x ^(2) - x+1=0,` and the matrix `A=[{:(1,1,1),(1, alpha , alpha ^(2)), (1, alpha ^(2), alpha ^(4)):}]` and matrix `B= [{:(1,-1, -1),(1, alpha, - alpha ^(2)),(-1, -alpha ^(2), - alpha ^(4)):}]` then the vlaue of |AB| is:

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