Compute the determinant of the matrix that's obtained from A by applying the indicated row operation:

Question

Suppose A ∈ M₃ is a matrix with det(A) = -2

The following row operations:

a) R₁ - 7R₂

b) 3R₂

c) R₃ ⇄ R₁

Answer 1

a) Adding a scalar multiple of one row to another row does not change the determinant. So the matrix resulting from this operation has determinant -2

b) Multiplying a row by a scalar multiplies the determinant by that scalae. So the matrix resulting from this operation has determinant 3*(-2) = -6

c) Interchanging rows multiplies the determinant by -1. So the matrix resulting from this operation has determinant +2