Consider the "reverse identity matrix", let's denoted it by $\bf I'$, by which I mean the $n\times n$ matrix with zeros everywhere except on the diagonal from bottom left to the top right (i.e. $(\delta'_{ij})$ where $\delta'_{ij} = 1$ if $i+j = n + 1$ and $0$ otherwise). For example with $n=4$,
$$ \mathbf{I'} = \begin{pmatrix} 0&0&0&1\\ 0&0&1&0\\ 0&1&0&0\\ 1&0&0&0 \end{pmatrix}. $$
Question: Is there an easy way to express $\bf I'$ in terms of commonly used matrices?
We usually try to express everything using $\bf I$, the usual identity matrix, and $\bf J$, the matrix consisting of all ones, and maybe the adjacency matrices of common graphs such as $K_n$. Also it goes without saying that easy operations such as transpose and so on are allowed.