Question: ```
\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{mathtools}
\begin{document}
\renewcommand{\arraystretch}{1.2}
\newcommand{\minus}{\scalebox{0.4}[1.0]{$-$}}
\[
\begin{bmatrix*}[r]
  0&  \minus\frac{1}{2} &\frac{1}{2} \\
  \minus\frac{1}{2}&  0&\minus\frac{1}{2}\\
  \frac{1}{2}&  \minus\frac{1}{2}&0
\end{bmatrix*}
\]
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/1yvlc.png)](https://i.stack.imgur.com/1yvlc.png)

How to reduce the number “0” size to fit fraction "1/2"? (reduce height of "0" ?)

---

update sample

As below photo shows the proportion close to 1/3

[![enter image description here](https://i.stack.imgur.com/Ofr0I.jpg)](https://i.stack.imgur.com/Ofr0I.jpg)

Answer: 
A good solution, in my opinion, to reduce the size discrepancy between fractions (in text mode by default) and ordinary numbers is to use the medium-sized fractions from `nccmath`, which are ca 80 % of \displaystyle:

```
\documentclass{article}
\usepackage{nccmath, mathtools} % for 'bmatrix*' env.
\usepackage{makecell}

\begin{document}

    \[ \setcellgapes{3pt}\makegapedcells
    \begin{bmatrix*}[r]
    \phantom{-}0 & -\mfrac{1}{2} & \mfrac{1}{2} \\
     -\mfrac{1}{2} & 0 & -\mfrac{1}{2} \\
    \mfrac{1}{2} & -\mfrac{1}{2} & 0
    \end{bmatrix*} 
    \]%

\end{document}

```

[![enter image description here](https://i.stack.imgur.com/i86b7.png)](https://i.stack.imgur.com/i86b7.png)
I would say that your sample actually suggests the opposite: "I want to preserve regular size even for numerators and denominators". Use `\dfrac` instead of `\frac`.

Also, why do you have special treatment for minus? Why the `-` isn't enough?

```
\documentclass{article}

\usepackage{amsmath}
\usepackage{array}
\usepackage{mathtools}

\begin{document}
\renewcommand{\arraystretch}{2}
\[
  \begin{bmatrix*}[r]
    0             &  -\dfrac{1}{2} & \dfrac{1}{2}  \\
    -\dfrac{1}{2} &  0             & -\dfrac{1}{2} \\
    \dfrac{1}{2}  &  -\dfrac{1}{2} & 0
  \end{bmatrix*}
\]
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/QLU1E.png)](https://i.stack.imgur.com/QLU1E.png)