# Thread: Show that the product of two upper triangular matrices is upper triangular matrix

1. ## Show that the product of two upper triangular matrices is upper triangular matrix

Show that the product of two upper triangular matrices is upper triangular matrix.

I know this is true because in the lower part each term will be multiplied by 0 (so in the lower part each element will be 0(a)+0(b)...+0(z))

My question is how do you actually write this?

2. Hint :

If $\displaystyle A=(a_{ij})$ and $\displaystyle B=(b_{ij})$ are $\displaystyle n\times n$ matrices, and $\displaystyle AB=(c_{ij})$ use:

$\displaystyle c_{ij}=\displaystyle\sum_{k=1}^n{a_{ik}}b_{kj}$

Fernando Revilla

3. Originally Posted by Jskid
Show that the product of two upper triangular matrices is upper triangular matrix.

I know this is true because in the lower part each term will be multiplied by 0 (so in the lower part each element will be 0(a)+0(b)...+0(z))

My question is how do you actually write this?
And the characterization of "the lower half is zero" in terms of these $\displaystyle a_{i,j}$s' Dr. Revilla speaks of.