Inverse of a Matrix
Definition: Let A be a square matrix of order n x n(square matrix). If there exists a matrix B such that
Then B is called the inverse matrix of A.
Conditions
A n x n is invertible (non-singular) if:
- Ax=0 has a unique solution
- There is a B matrix such that A B = In
- Ax=b has a unique solution for any b---x=A^-1 b
Properties
- (AB)^-1
$ \left(\begin{array}{cccc}1&2&3&4\\5&6&7&8\end{array}\right) $
