Let $(R,+,*)$ be an unitarian ring.
If $A$ is an unitarian ring.
$a,b$ are from $R$ and $a*b$ is invertible, it results that $a$ is invertible and $b$ is invertible?
(b) If $a$ is from $R$ and $a^n=a * a*...* a$ ($n$ or) is invertible,it results that $a$ is invertible?
(c) If $a$ is invertible to left and it isn't zero divisor to right,prove that $a$ is invertible.
(a) Here I tried to find a counterexample to that affirmation, but I couldn't find it.
(b) I wrote the definition of invertibility for a^n,but from that I couldn't find anything.
(c) I wrote the definition of invertibility and for non-zero divisibility for $a$, but I couldn't deduce anything from it.
Please, could you help me?