Let $H_n$ be the space of all $n\times n$ matrices $A = (a_{i,j})$ with entries in $\mathbb{R}$ satisfying $a_{i,j} = a_{r,s}$ whenever $i+j = r+s$ $(i, j , r , s = 1, 2, \ldots, n)$. What would be dimension of $H_n$ as a vector space over $\mathbb{R}$?
i have options for the dimension
1 - $n^2$
2- $n^2-n+1$
3 - $2n+1$
4- $2n-1$
I am finding difficulty in identifying the matrix $A$ . thanks for support