A simple Linear Algebra question that seems so hard

[qwerty11]

Homework Statement

Is the statement true or sometimes false. Justify your answer:

The determinant of a matrix is unchanged if the columns are written in reverse order.

Homework Equations

The Attempt at a Solution

I understand that the only thing that is changed is the sign (negative to positive or visa-versa), but do not understand the proof of how.

 

[dacruick]

how do you find the determinant of a matrix?

 

[qwerty11]

One way would be via cofactor expansion.

I.e. 3x3 matrix determinant =a11C11+a12C12+a13C13

 

[dacruick]

okay good. so if you switched the columns, how would the cofactor expansion change?

 

[dacruick]

and calculate out those cofactors when you do it.