math - (A^x) % Mod == (A^(x % (Mod - 1)) % Mod. if Mod is Prime. True when A is a matrix? -

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(a^x) % mod == (a^(x % (mod - 1)) % mod. if mod prime.

is property true when 'a' matrix?

suppose a=
1 0 1
1 0 0
0 1 0

x=1000000007 , mod=1000000007

then ( a^x ) % mod is

097981108 432592815 646971665
646971665 451009450 432592815
432592815 214378850 451009450

but (a^1)%mod [ as, ( x % (mod-1) )=1 ] same matrix.

that property ( assuming understood correctly ) false.

just consider

a = 1 0 // 0 2 x = 3 mod = 2

you 

a^3 % 2  != a^0 % 2

because 

left : 1 0 // 0 0  right: 1 0 // 0 1

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