Minor of an element of a determinant. Let |A| = |a_ij| be a determinant of order n. The minor of a_ij, the element in the ith row and jth column of |A|, is the determinant that is left by deleting the ith row and the jth column. It is denoted by M_ij.

For example, given the 3x3 determinant



The minor of a₁₁ is M₁₁ = 

The minor of a₁₂ is M₁₂ =  

and so on.

Cofactor of an element of a determinant. Let |A| = |a_ij| be a determinant of order n. The cofactor of a_ij, denoted C_ij or A_ij, is defined as (-1)^i+j  M_ij, where I + j is the sum of the row number  I and column number j in which the entry lies.

Thus



For example, the cofactor of a 12 in the 3 x 3 determinant



is C₁₂ = (-1)¹⁺² 

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