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
by adding -2.5 times the first row to the second gives:
Here's my confusion. To eliminate the first 1.5 I can either add 1/2 the first row to the third or -5.75/1.5 the second row to the third. Depending on which route I take the last element in the third row will be differnt, and when I multiply the numbers along the diagonal I will get 60 or 72 for the determinant.