Consider the following statements: (a) If any two rows or columns of a determinant are identical, then the value of the determinant is zero. (b) If the corresponding rows and columns of a determinant are interchanged, then the value of the determinant does not change. (c) If any two rows (or columns) of a determinant are interchanged, then the value of the determinant changes in sign. Which of these are correct ?

Question

Consider the following statements: (a) If any two rows or columns of a determinant are identical, then the value of the determinant is zero. (b) If the corresponding rows and columns of a determinant are interchanged, then the value of the determinant does not change. (c) If any two rows (or columns) of a determinant are interchanged, then the value of the determinant changes in sign. Which of these are correct ? (A) (a) and (b) (B) (b) and (c) (C) (a) and (c) (D) all the above

Tardigrade Admin · Accepted Answer

By the properties of determinant, all the three statements are correct.