Matrix A is such that A2=2A−I, where I is the Identity matrix. Then for n≥2, An is equal to
nA−(n−1)I
nA−I
2n+1A−(n−1)I
2n−1A−I
A2=2A−IA3=A2.A=(2A−I)A=2A2−IA=2(2A−I)−AA3=3A−2IMultiplying with A,A4=A3.A=(3A−2I)A=3A2−2A=3(2A−I)−2AA4=4A−3IIn general, An=nA−(n−1)I