Suppose we are given an arbitrary ring $R$. Then the set $M_n(R)$ of all square matrices with elements from $R$, together with usual matrix addition and multiplication forms a ring. If R is a unitary ring then $M_n(R)$ too.
My question seems to be very trivial but is it possible that $M_n(R)$ has unity while $R$ hasn't?
Thanks in advance.