Chapter 10 - Systems of Equations and Inequalities - Section 10.3 Systems of Linear Equations: Determinants - 10.3 Assess Your Understanding - Page 760: 6

False

We must consider Theorem-14 which states that: When any row or any column of a determinant is multiplied by a nonzero number (let us say $a$), then the value of the determinant is also changed by a factor of $a$. This means that the given statement is false, since it claims that the determinant remains unchanged.