Class 12 Maths Determinants Determinant

Determinant

The determinant of a matrix is a special number that can be calculated from a square matrix. The determinant of a matrix A is denoted det(A), det A, or |A|.

 

 

The determinant tells us things about the matrix that is useful in systems of linear equations, helps us find the inverse of a matrix, and is useful in calculus, Computer Science, Chemistry, Geoemetry and more.

 

Properties of Determinants

  • The determinant is a real number, it is not a matrix.
  • The determinant can be a negative number.
  • It is not associated with absolute value at all except that they both use vertical lines.
  • The determinant only exists for square matrices (2×2, 3×3, ... n×n). The determinant of a 1×1 matrix is that single value in the determinant.
  • The inverse of a matrix will exist only if the determinant is not zero.
  • For matrix A, |A| is read as determinant of A and not modulus of A.
  • Only square matrices have determinants

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