Chapter 12.4, Problem 53E

Suppose that $a\ne 0$.

(a) If $a\cdot b=a\cdot c$, does it follow that $b=c?$

(b) If $a\times b=a\times c$, does it follow that $b=c?$

(c) If $a\cdot b=a\cdot c$, and $a\times b=a\times c$, does it follow that $b=c?$