Which of the following is not a property of determinant?

The correct option is: "The value of determinant changes if all of its rows and columns are interchanged".

Let us analyze the properties of determinants to understand why this statement is incorrect (and hence, is not a property of determinants):

1. Transpose Property (Interchanging all rows and columns):
When all the rows and columns of a determinant are interchanged, we are taking the transpose of the underlying matrix. A fundamental property of determinants states that the determinant of a matrix is equal to the determinant of its transpose. That is, if A is a square matrix and A^T is its transpose:

$$det\left(A\right)=det\left(A^T\right)$$

Therefore, the value of the determinant does not change when all rows and columns are interchanged. This makes the statement in the selected option false, meaning it is not a property of determinants.

2. Verification of the other options (which are true properties):
• "The value of determinant changes if any two rows or columns are interchanged": Interchanging any two rows or two columns multiplies the determinant by $-1$, which changes its sign (and thus its value, unless it is zero). This is a valid property.
• "The value of determinant is zero if any two rows and columns are identical": If any two rows (or columns) are identical, the determinant evaluates to zero. This is a valid property.
• "The value of determinant gets multiplied by k, if each element of row or column is multiplied by k": Factoring out a scalar k from any single row or column multiplies the value of the entire determinant by k. This is also a valid property.