# What is the simplest way to solve determinant of a $n \times n$ matrix by upper and lower triangular matrices?

I know the basic rules to solve for the determinant of an $n \times n$ matrix using upper and lower triangular matrices, but what is the simplest way?

• @robert-lewis thanks for editing. sorry for my bad english ability. – RezaOnline Nov 17 '14 at 6:32
• What do you mean by "simplest"? Easiest to do with a pencil and paper, or easiest to do with a computer? Or perhaps the fastest to do with a computer? – Omnomnomnom Nov 17 '14 at 6:34
• Hey, really glad to help out. Don't worry about your English, just keep writing it! Cheers! – Robert Lewis Nov 17 '14 at 6:34
• @Omnomnomnom i mean the easiest and fastest solution for this issue. i know the main solution but i search for a better method. – RezaOnline Nov 17 '14 at 6:37
• @RezaOnline are you aware of how to compute determinants by Gaussian elimination? You could just row-reduce until you have an upper-triangular matrix. – Omnomnomnom Nov 17 '14 at 6:43