Another example: Let $n$ be a positive integer, and consider the subring of the opposite of the ring of $n$-by-$n$ matrices over a commutative unital ring $(A, +, \cdot)$ consisting of those matrices all of whose rows, except at most for the first, are zero; this has $|A|^{n-1}$ right identities.

I was browsing some "What is...?" threads, and bumped in here: Let $n$ be a positive integer, and consider the subring of the opposite of the ring of $n$-by-$n$ matrices over a commutative unital ring $\mathbb A = (A, +, \cdot)$ consisting of those matrices all of whose rows, except at most for the first, are zero; this has $|A|^{n-1}$ right identities, given by those matrices whose first row is any vector of $A^n$ with first element equal to $1_\mathbb{A}$.