(From Determinants. Prove the proposition without using Cofactors/Cramer's rule.)
See Attached© BrainMass Inc. brainmass.com March 4, 2021, 8:35 pm ad1c9bdddf
Please see the attachment.
We should use the following properties of determinant.
1. Switching two rows or columns changes the sign.
2. Scalar multiplication of a row by a constant multiplies the determinant by .
3. Multiplies of rows and columns ...
This is a proof regarding determinants of elementary matrix and arbitrary square matrix.