Problem: Proof that squares are non-negative

Problem

Prove that for any real number $a$ ,

$$a^2≥0$$

You can use the following:

• If $a≥0$ and $b≥0$ then $a⋅b≥0$
• $(-a)⋅\left( -b \right)=a⋅b$ .

Hint: Consider three cases: $a<0$ , $a=0$ and $a>0$ .