Question

اگر$ A^{2} =I$ باشد آنگاه:

$$ A^{2n} =?$$

$$ A^{2n+1} =?$$

$n \in N$

Answer 1

$$A ^{2n} = \underbrace{A^{2} \times... \times A^{2} }_{n} =I \times ... \times I=I $$ $$A ^{2n+1} = \underbrace{A^{2} \times... \times A^{2} }_{n} \times A =I \times ... \times I \times A=A $$