Algebra/Division is not commutative

Division is not commutative. That means usually a ÷ b is not equal to b ÷ a.

But what if it were?

$a÷b=b÷a⟺\text{(rewrite as fractions)}$

$\frac{a}{b}=\frac{b}{a}⟺\text{(multiply both sides by}ab)$

$a^2=b^2⟺\text{(take both square roots)}$

$a=\sqrt{b^2}⟺\text{ OR }a=-\sqrt{b^2}$

$a=b\text{ OR }a=-b⟺$

$a÷b=1\text{ OR }a÷b=-1$

So division is not commutative because there are only two very special cases when the answer is the same if you reverse the order of operation: when the answer (quotient) is 1 or when the answer is -1.