Let A be a square matrix.
a. If a multiple of one row of A is added to another row to produce a matrix B, then detB = detA.
b. If two rows of A are interchanged to produce B, then detB = -detA.
c. If one row of A is multiplied by k to produce B, then detB = k * detA.
There were issues when copy pasting but I think I correctly replaced the special characters. My question is, would someone be able to give an example of 'a', and also can it be any two rows of A? Like what if I had a 5 x 5 matrix called A and if I perform the following interchanges, would det A = det A?
- Replace row 1 with 3
- Replace row 2 with 4
After those two, would I end back up with the same det?