Matrix $A$ satisfies $A^2=2A-I$ where $I$ is the identity matrix. For $n \geq 2$, $A^n$ is equal to $(n\in N)$

Question

$\begin{array}{1 1}(a)\;nA-I&(b)\;2^{n-1}A-(n-1)I\\(c)\;nA-(n-1)I&(d)\;2^{n-1}A-I\end{array}$