Matrix reciprocal positive to prove $λ_{max⁡}=n$ Suppose we have $n\times n$ matrix $A$ having only positive elements and satisfying the property $a_{ij}=1/a_{ji}$ (a matrix satisfying this property is called a reciprocal matrix).
If its largest eigenvalue $λ_{max}$ is equal to $n$, then the matrix $A$ satisfies the property (consistency property) $a_{ij}a_{jk}=a_{ik}$ where $i,j,k=1,2,...,n$.

I already found an example of $5\times 5$ reciprocal matrix  to show this condition:
\begin{bmatrix}1&1/2&1&1&1/4\\2&1&2&2&1/2\\1&1/2&1&1&1/4\\1&1/2&1&1&1/4\\4&2&4&4&1\end{bmatrix}
It has simple characteristic equation $λ^5-5λ^4=0$, so the eigenvalues of matrix $A$ are $λ=0$ and $λ=5$ and it's shown that $λ_{max}=n=5$.
Is there anyone can help me to give another positive reciprocal matrix example  that has simple characteristic equation and integer number as its eigenvalues ($4\times 4, 5\times 5$ or $6\times 6$ matrix)?

$$\pmatrix{1&2&3&4\cr1/2&1&3/2&2\cr1/3&2/3&1&4/3\cr1/4&1/2&3/4&1\cr}$$
