seek a special matrix
I am seeking the following example, maybe it is easy to construct, but I
have no idea now besides aimless computation.
Could anyone give me a matrix $A\in SL_n(\mathbb{Z})$ for some $n$, such
that $A$ has an eigenvalue $\lambda$ such that $|\lambda|\geq 2$ and the
eigenspace correspondence to $\lambda$ contains a $n$-column vector with
all entries belong to integers.
Thanks in advance!
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