Question

Determine is the following True or False: “If ab is a unit, then a, b are units”?

Answer 1

It's true because if ab is unit then $\left(ab\right)\left(b^{-1}a^{-1}\right) = \left(aa^{-1}\right)\left(bb^{-1}\right) = 1 \Rightarrow \left\{ \begin{array}{l} aa^{-1} = 1 \\ bb^{-1} = 1 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} a \text{ is unit} \\ b \text{ is unit} \end{array} \right.$

Answer: True.