Matrix A such that A2 =2A - I where I is the identity matrix, then for n≥2, An is equal to

Given A2 =2A - INow A3=AA2=A(2A−I)=2A2−A=2(2A−I)−A=3A−2IA4=AA3=A(3A−2I)=3A2−2A=3(2A−I)−2A=4A−3IFollowing this, we can say An=nA−(n−1)I