I am trying to figure out different ways og getting the eigenvalues so i will be able to do it quickly in an exam. I am wondering if all my reasoning is correct because i am still making a few mistakes.

1)row operations do not affect the determinant if we multiply be -1, each time we change a row.

2)if we divide a row by a constant what do i do to get the right answer for the determinant?

3) column operations do not affect the determinant