# Determinant 3

• March 28th 2009, 01:01 AM
james_bond
Determinant 3
In a $2n$-dimensional matrix $a_{ij}=\begin{cases}1\text{ if }i\le n\text{ and }j\ge n+1\text{ or }i\ge n+1\text{ and }j\le n\\0\text{ otherwise}\end{cases}$
What's the determinant?
• March 28th 2009, 11:53 AM
NonCommAlg
Quote:

Originally Posted by james_bond

In a $2n$-dimensional matrix $a_{ij}=\begin{cases}1\text{ if }i\le n\text{ and }j\ge n+1\text{ or }i\ge n+1\text{ and }j\le n\\0\text{ otherwise}\end{cases}$
What's the determinant?

the determinant is -1 for n = 1 and 0 for n > 1 because for n > 1 the first and the second row of the matrix are equal.