If A = [ 1 0 0 ]
If A =
[ 1 0 0 ]
[ 0 -1 0 ]
[ 1 0 1 ]
then the matrix for A⁶ is __________.
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Correct answer: (D) [ 1 0 0 ] [ 0 1 0 ] [ 6 0 1 ]
Explanation
Squaring gives row 3 = [2, 0, 1] and the middle entry (-1)² = 1. In general A^n has row 3 = [n, 0, 1] and middle entry (-1)^n, so A⁶ has row 3 = [6, 0, 1] and middle entry 1.