# A note on products of quadratic matrices of singular type

## TL;DR

This paper offers a new proof of a theorem related to the products of idempotent and square-zero matrices, and characterizes products of singular quadratic matrices using existing results.

## Contribution

It presents an alternative, self-contained proof of Botha's theorem and provides a comprehensive characterization of products of singular quadratic matrices.

## Key findings

- Proof of Botha's theorem is simplified and clarified.
- Characterization of products of singular quadratic matrices established.
- Enhanced understanding of matrix product structures in linear algebra.

## Abstract

I provide an alternate and self-contained proof of Botha's theorem on products of idempotent and square-zero matrices where the product contains two square-zero factors, and provide a conclusive characterisation of products of singular quadratic matrices based on previous results.