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M = MatrixSpace(ZZ,4,4) for A in M: if A.determinant()!=0: p=A.eigenvalues() o=list(p) for e in o: X = Set([1,2,3,4]) for i,j in X: if e[i]*e[j]==1: print(A)

I am trying to find those 4 by 4 nonsingular integer matrices which satisfy the following property: Suppose that if $\lambda$ is an eigenvalue of $A$ iff $\frac{1}{\lambda}$ is also an eigenvalue of $A$ with the same multiplicity as that of $\lambda$. How to obtain that class of matrices?

```

 M = MatrixSpace(ZZ,4,4)
 for A in M:
  if A.determinant()!=0:
     p=A.eigenvalues()
     o=list(p)
     for e in o:
         X = Set([1,2,3,4])
         for i,j in X:
             if e[i]*e[j]==1:
                    print(A)
print(A)

I am trying to find those 4 by 4 nonsingular integer matrices which satisfy the following property: Suppose that if $\lambda$ is an eigenvalue of $A$ iff $\frac{1}{\lambda}$ is also an eigenvalue of $A$ with the same multiplicity as that of $\lambda$. How to obtain that class of matrices?

```

 M = MatrixSpace(ZZ,4,4)
 for A in M:
  if A.determinant()!=0:
     p=A.eigenvalues()
     o=list(p)
     for e in o:
         X = Set([1,2,3,4])
         for i,j in X:
             if e[i]*e[j]==1:
                 print(A)

I am trying to find those 4 by 4 nonsingular integer matrices which satisfy the following property: Suppose that if $\lambda$ is an eigenvalue of $A$ iff $\frac{1}{\lambda}$ is also an eigenvalue of $A$ with the same multiplicity as that of $\lambda$. How to obtain that class of matrices?