  In linear algebra applications, elementary matrices hold a significant role.
This paper presents a diagrammatic representation of all $2^m\times 2^n$-sized
elementary matrices in algebraic ZX-calculus, showcasing their properties on
inverses and transpose through diagrammatic rewriting. Additionally, the paper
uses this representation to depict the Jozsa-style matchgate in algebraic
ZX-calculus. To further enhance practical use, we have implemented this
representation in \texttt{discopy}. Overall, this work sets the groundwork for
more applications of ZX-calculus such as synthesising controlled matrices
[arXiv:2212.04462] in quantum computing.
