How Does Scaling a Column Affect the Determinant of a Matrix?

[Reeses]

If the determinant of a 3x3 matrix A is det(A)=5, and the matrix B is obtained from A by multiplying the first column by 8, then det(B)=?

I really haven't tried anything for this question; I'm not even sure where to start.

 

[Unco]

Hi Reeses,

Start by reviewing your class notes or text: what effect does multiplying a column of a matrix by a scalar have on its determinant?

 

[VeeEight]

You might even want to try to figure it out before consulting your notes. Take a 3x3 identity matrix and see what effect multiplying a single column (or more than a single) by a scalar has on the determinant.