Originally Posted by

**superdude** 1) Do all square matrices have a unique determinant?

2) If the answer to the above question is yes, then what part of the following procedure am I over looking?

I am trying to use "computation via reduction to a triangular form" to find the determinant of $\displaystyle \left[\begin{matrix}

4 & -3 & 5 \\

5 & 2 & 0 \\

2 & 0 & 4

\end{matrix} \right]

$

by adding -2.5 times the first row to the second gives: $\displaystyle \left[\begin{matrix}

4 & -3 & 5 \\

0 & -5.75 & -6.25 \\

0 & 1.5 & 1.5

\end{matrix} \right]

$