Let $\mathbb{R}^N$ be a D816: Euclidean real Cartesian product.
Let $I_E$ be an D41: Indicator function for $E \subseteq \mathbb{R}^N$ in $\mathbb{R}^N$.
Let $a, x \in \mathbb{R}$ each be a D993: Real number such that

(i)	$a \neq 0$

Then

(1)	\begin{equation} I_E(a x) = I_{\frac{1}{a} E} (x) \end{equation}
(2)	\begin{equation} \textstyle I_E (\frac{1}{a} x) = I_{a E} (x) \end{equation}