MathematicsLet A=(010100011). Then the sum of all elements of A100 equals

Let $A = (\begin{array}{lll} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 1 \end{array}) .$ Then the sum of all elements of $A^{100}$ equals

A
101
B
103
C
102
D
100

Solution:

$\begin{array}{lll} 0 & 1 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 1 & 1 \\ A & A \end{array}$ $\begin{array}{lllllllll} 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 2 & 1 & 2 & 2 & 1 \\ A^{2} & A^{3} & A^{4} \end{array}$

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Type of relations_mathematics