A = 2 x 2

Question

-1 0
0 -1

find n that
A^n * B = C

B = 2 x 1
0
1

C = 2 x 1
1
0

answer is 6, but I don't know why

find A^2014

the answer is
0 1
-1 0
but I don't know why

Answer 1

Beats me.
A to any even power is the identity matrix
1 0
0 1
for exaample
A^2
-1 0
0 -1
times itself
-1 0
0 -1
is
1 0
0 1
that times A will be A
that times A will be identity matrix again