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I have a question regarding upper triangular matrix.

I know that if AB is upper triangular then the |AB| equals to the diagnoal multiplication, but It doesn't seem to help me here.

If AB is upper triangular and non-singular then A and B both upper triangular?

Notice that A and B are both square.

I can't choose AB = 0 becuase its signular....

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    Never mind, didn't read the question properly...2012-10-29

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No, $A$ and $B$ does not necessarily have to be upper triangle. For example, $\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$

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    damn missed you answer till now. Thank you very much !2012-10-29