Determinants — Class 12 Mathematics

The determinant is a scalar associated with a square matrix that captures key information about it. For a matrix the determinant is ; for larger matrices it is computed by expansion along a row or column using minors and cofactors. This chapter covers properties of determinants, the use of determinants to find the area of a triangle, the adjoint () of a matrix, and the inverse via , valid when . A matrix is invertible (non-singular) exactly when its determinant is non-zero. Determinants are then applied to solve systems of linear equations using Cramer's-style matrix methods (), linking algebra to geometry and to consistency of equations.