Let $\mathbf{A}$ be a matrix and $\mathbf{x}$ be a non-zero vector such that \[\mathbf{A} \mathbf{x} = 2 \mathbf{x}.\]Then we have that \[\mathbf{A}^7\mathbf{x} = a \mathbf{x}\]some value of $a$. What is $a$ equal to?
Think about
\(\mathbf{A^7}\mathbf{x}= \mathbf{A^6}(\mathbf{A}\mathbf{x})\)
