1. Cofactor Method for Inverses
• Let A = (aij) be an nxn matrix
• Recall, the co-factor Cij of element aij is:
Cij = (-1)i+j
|Mij|
• Mij is the (n-1) x (n-1) matrix made by
removing the ROW i and COLUMN j of A
2. Cofactor Method for Inverses
• Put all co-factors in a matrix – called the
matrix of co-factors:
C11 C12 C1n
C21
Cn1
C22
Cn2
C2n
Cnn
3. Cofactor Method for Inverses
• Inverse of A is given by:
A-1
= (matrix of co-factors)T1
|A|
1
|A|
C11 C21 Cn1
C12
C1n
C22
C2n
Cn2
Cnn
=