Chapter 4 - Eigenvalues and Eigenvectors - 4.2 Determinants - Exercises 4.2 - Page 282: 28

$-15$

After swapping the first and third rows the matrix will become triangular, with the sign of the determinant changing. We know that if a matrix is triangular, its determinant equals the product of the diagonal entries, hence here: $-D=3\cdot5\cdot1=15$, thus $D=-15$