New to Linear Algebra and trying to get decent at proofs. Any help is appreciated.
Is this a valid way to prove the Cancellation Law of Multiplication? I've only seen it done some alternative way that doesn't make much intuitive sense to me.
Given: For all real numbers $x,y,k$ where $k\neq 0$ .
If $kx = ky$, then $x = y $
*First, $ky, kx$ are also real numbers by the Closure property of Multiplication
$kx = ky$ : Implication
$k(1/k)x = k(1/k)y $: Substitution
$(k(1/k))x = (k(1/k))y $: Associative Property of Multiplication
$(1)x = (1)y$ : Multiplicative Inverse
$x = y$ : Multiplicative Identity