Question

( begin{array}{l}A=left[begin{array}{ll}w & 0 0 & omegaend{array}right] A^{2}=left[begin{array}{ll}omega^{2} & 0 0 & omega^{2}end{array}right] A^{3}=left[begin{array}{ll}omega^{2} & 0 0 & omega^{2}end{array}right]left[begin{array}{ll}omega & 0 0 & omegaend{array}right]=left[begin{array}{ll}omega^{3} & 0 0 & omega^{3}end{array}right]=left[begin{array}{ll}1 & 0 0 & 1end{array}right]=I A^{100}=A^{99} A=left(A^{3}right)^{33} A=(I)^{33} A & =I cdot A=Aend{array} )

# If A _ 0 0 1 100 , which o is cube root of unity, then what is A 100 equal to ? (a) A (b)-A (d) Identity matrix (c) Null matrix

Solution