---
type: "problem"
title: "Determinant of a matrix with consecutive integers"
slug: "determinant-of-a-matrix-with-consecutive-integers"
author: "ancient-tree"
tags: ["determinant", "matrix"]
difficulty: 29
qualityStatus: "unreviewed"
listed: true
origin: "Unknown"
originChapter: ""
originPage: ""
originNote: ""
license: "CC BY-SA 4.0"
---

Consider the matrices : $$A_1=(1), A_2=\left(\begin{array}{ll}
1 & 2 \\
3 & 4
\end{array}\right), A_3=\left(\begin{array}{lll}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{array}\right), \ldots$$ 
What is the determinant of $A_n$ ?