# How to prove the determinant of a matrix is zero?

• April 13th 2010, 12:50 PM
Magnolia
How to prove the determinant of a matrix is zero?
The matrix M satisifies the following properties:
1. m_{ii}>0
2. m_{pq}m_{qp}=m_{pp}m_{qq}
3. m_{ij}m_{ji}=0 or m_{ii}m_{jj}, i,j not equal to p and q.
• April 14th 2010, 02:59 AM
HallsofIvy
Do a row reduction: look at what happens when you subtract, say, $\frac{a_{12}}{a_{11}}$ times the first row from the second. Try it with a 2 by 2 matrix first.
• April 14th 2010, 06:35 AM
Magnolia