Properties of Determinants And Some Important Determinants to Remember

Properties of Determinants:-

  1. Determinant of a matrix is same as the determinant of its transpose.
  2. If two rows or columns of a determinant are interchanged the determinant changes its sign.
  3. If the elements of a row (column) of a determinant are multiplied by a constant K, then the determinant will be multiplied by the same constant. For example,
    Property of Determinant

    If A is a square matrix of order n, then

  4. If all the elements of a row (column) of a determinant are zeros, then the value of that determinant is also zero.
  5. If two rows (columns) of a determinant are equal then value of that determinant is zero.
    Note:- If two rows (2 columns) of a determinant are proportionate then its value is zero.
  6. If the elements of a row (column) of a determinant are sums of two elements then the determinant can be expressed as the sum of two determinants. That is for example,
    Property-of-Determinant
  7. If the elements of a row (column) of a determinant are added to or subtracted from the corresponding elements of some other row (column) then the determinant remains unchanged.
    Property of a Determinant
  8. If the products of the elements of a row (or column) of a determinant with a constant K are added to the corresponding elements of some other row (or column), then the determinant remains unchanged.
    elements-cofactors-product-in-a-Determinant-Property
  9. Sum of the products of the elements of a row in a square matrix and the co-factors of the corresponding elements of some other row (column) is zero.
  10. If the rows or columns of a determinant are changed without disturbing a cyclic order, then the determinant remains unchanged. That is,
    Determinant Remains Unchanged when rows or columns of a determinant are interchanged with disturbing cyclic order
  11. Determinant of a null matrix is 1.
    Determinant-of-unit-matrix-is-unity
  12. Determinant of a null matrix of the order 3X3 is zero.

Some Important Matrices Determinants to be Remembered for competitive exams:-

Some Important Determinants to be Remembered


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