How Do Row Operations Affect Matrix Determinants?

[LaraCroft]

Homework Statement

If the determinant of a 3 x 3 matrix A is det(A) = 10, and the matrix B is obtained by multiplying the third row by 8, then det(B) = ___?

If the determinant of a 5 x 5 matrix A is det(A) = 9, and the matrix C is obtained from A by swapping the second and fourth rows, then det(C) =___?

Homework Equations

Ok, so do I use a generic matrix, or what? SO confused...

The Attempt at a Solution

 

[tiny-tim]

Hi LaraCroft!

Useful tip: write out a few matrices (easy ones, with lots of zeros ), and see what happens …

then you can set about proving why