How we can construct the following $n\times n$ matrix $A=(a_{ij})$ such that $a_{ij}=1$ when $j-i\equiv$1 mod $n$; $a_{ij}=-1$ when $j-i\equiv$-1 mod $n$ and $a_{ij}=0$ otherwise. I need for $n=10$.
How we can construct the following $n\times n$ matrix $A=(a_{ij})$ such that $a_{ij}=1$ $a_{ij}= 1$ when $j-i\equiv$1 mod $n$; $a_{ij}=-1$ $a_{ij}= -1$ when $j-i\equiv$-1 mod $n$ and $a_{ij}=0$ otherwise. I need for $n=10$. $n=10$.