Swap two rows (columns) and change the sign

Transpose, the value remains unchanged

If there is a row (column) with all zero elements, the value is zero.

If there are two rows (columns) whose elements correspond to proportions, the value is zero.

If the element of a row (column) is the sum of two numbers, it can be split into the sum of two determinants

Add k times of a row (column) to another row (column), the value remains unchanged

If the elements of a certain row (column) have a common factor k, they can be mentioned outside the determinant symbol. In other words, if you use a number k to multiply the determinant, you can multiply this number to a certain row (column) of the determinant.

Level 4 and above

Second and third order determinants