Property 5 : All elements in a row (column) of the determinant are multiplied by the number and then added to the elements at the corresponding position in another row (column), and the value of the determinant remains unchanged.
　　For example , multiply the number by the -th column and add it to the -th column, then we have

　　Prove: According to determinant property 4 and corollary 3 , we have

　　Note: Multiply the -th row of the determinant by the number and add it to the -th row, written as

;

Multiply column of the determinant by number and add it to column , written as

.