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 \(a>0\) .