Question

Each equation in Exercises 1-4 illustrates a property of determinants. State the property

\(\left| {\begin{array}{*{20}{c}}{\bf{0}}&{\bf{5}}&{ - {\bf{2}}}\\{\bf{1}}&{ - {\bf{3}}}&{\bf{6}}\\{\bf{4}}&{ - {\bf{1}}}&{\bf{8}}\end{array}} \right| = - \left| {\begin{array}{*{20}{c}}{\bf{1}}&{ - {\bf{3}}}&{\bf{6}}\\{\bf{0}}&{\bf{5}}&{ - {\bf{2}}}\\{\bf{4}}&{ - {\bf{1}}}&{\bf{8}}\end{array}} \right|\)

Short answer

Due to row interchange, the determinant changes the sign.

Step-by-step solution

Recall the property of determinant

When the rows of the determinant are interchanged, the determinant changes the sign.

Apply the property for the given determinants

For the determinants, rows 1 and 2 interchanges, and the value of the determinant becomes negative.

So, due to row change, the determinant changes the sign.