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Consider the polynomial $p(x)=x^3-x^2+x-1$. How many *symmetric* matrices with integer entries are there whose characteristic polynomial is $p$? (Recall that the *characteristic polynomial* of a square matrix $A$ in the variable $x$ is defined to be the determinant of the matrix $(A-x I)$ where $I$ is the identity matrix.)

- $0$
- $1$
- $2$
- $4$
- Infinitely many