# what effect does this have on the deteriminant?

• Jan 28th 2010, 11:15 AM
superdude
what effect does this have on the deteriminant?
If the determinant of the matrix A is 3 then what is the determinant of det(4A)?

The answer involves something like this:
$4^2det(A)$
why does 4 get squared and come out in front?
• Jan 28th 2010, 02:24 PM
TKHunny
You're kidding, right?!

Did you try even one example?

Try a 2x2 matrix and see for yourself. It's called "exploration". (Speechless)
• Jan 28th 2010, 06:40 PM
tonio
Quote:

Originally Posted by superdude
If the determinant of the matrix A is 3 then what is the determinant of det(4A)?

The answer involves something like this:
$4^2det(A)$
why does 4 get squared and come out in front?

Basic properties of determinants, and it is $4^2$ only if the matrix is 2 x 2; in general, if the determinant is n x n, $\det (kA)=k^n\det A\,,\,\,k$ a scalar.

Tonio