Minors and Co-factors

To evaluate the determinant of order 3 or above, you need to define minors and co-factors.

Minors

Let |A| = |[a_ij]| be a determinant of order n. The minor of an arbitrary element a_ij is the determinant obtained by deleting the i^th row and j^th column in which the element a_ij stands. The minor of a_ij is denoted by M_ij.

Co-factors

The co-factor is a signed minor. The co-factor of a_ij is denoted by A_ij and is defined as

A_ij = (−1)^i+j M_ij

Determinant Expansion