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