Thread: Linear Algebra; prove the theorems on left and right inverses.

Prove that if the matrix has a right inverse, then for each
the equation has at least one solution. If has a left inverse,
then that equation has at most one solution.

Originally Posted by mathwizard

Prove that if the matrix has a right inverse, then for each
the equation has at least one solution.

let with identity matrix. then i.e. satisfies so there's at least one solution.

If has a left inverse, then that equation has at most one solution.

let and suppose that then so has at most one solution.