# How to prove the product of upper triangular matrices is upper triangular?

1. Jan 12, 2015

### Brucezhou

This seems easy but when I tried to do this, the best way I came up with is to list all entries and then do the multiplication work. Is there any better ,clearer and more simple way to do the proof?

2. Jan 12, 2015

### SteamKing

Staff Emeritus
Did you try to express the entries in the product matrix in terms of the dot products of the row of one matrix with the corresponding column in the second matrix?

3. Jan 12, 2015

### vela

Staff Emeritus
Suppose A is an upper triangular matrix with elements $a_{ij}$. Then you know that $a_{ij}=0$ if $i>j$. If C=AB where B is also upper triangular, you want to show that $c_{ij}=0$ if $i>j$.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted