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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?