1. Tardigrade
  2. Question
  3. Mathematics
  4. 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 ?

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Q. 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 ?

KCETKCET 2014Determinants

Solution:

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