(i) If a square matrix satisfies ``either or ,'' then is invertible, and has the unique inverse .
(ii) When and are invertible, we have the following properties:
(iii) If is invertible, the equation has the unique solution .
The function inv(A) computes the inverse of a matrix A,
Then the solution to
by inv(A) * b.
Besides, Matlab/Octave has the special operator ``
left division, which computes the solution immediately
A \ b.
In summary the following two commands give the same solution:
> inv(A) * b > A \ b
EXAMPLES 1. Let and . Then show that .
EXAMPLES 2. Find the inverse of
EXAMPLES 3. Solve the system