Determinant Prove...1

[mathdad]

Interchange columns 1 and 3 of a 3 by 3 determinant. Show that the value of the new determinant is - 1 times the value of the original determinant. How is this done?

 

[Romsek]

the easiest way is to write the column transposition as the product of the original matrix with an elementary matrix
and note the determinant of the product is the product of the determinants

 

[Dr.Peterson]

Interchange columns 1 and 3 of a 3 by 3 determinant. Show that the value of the new determinant is - 1 times the value of the original determinant. How is this done?

What have you learned about determinants that you might use? We don't know what's available to you.

Maybe you can use what you know about expansion by minors? Or maybe something in the definition of the determinant? It sounds like you are expected to use something specific to 3x3 matrices, rather than something general.