Property 3: Multiplying a row (column) of a determinant by a number is equivalent to multiplying the determinant by , that is

.

　　Proof : According to the definition of determinant , after multiplying the row by the number , the determinant is

　　Note: The row (column) is multiplied by , recorded as

(or ) .

　　Corollary 2: The common factor of all elements in a certain row ( column) of the determinant can be mentioned outside the determinant symbol.
　　Corollary 3: In a determinant, if there are two rows (columns) elements that are proportional, then the determinant must be equal to zero.

　　For example, the determinant

,

Since the corresponding elements in column and column are proportional, from Corollary 3, we can directly get

.