Matrix Operations

Question

Let E = [2, -1, 3, 0], & F = [0, 1, -1, 2]

Are E and F inverses of each other? Why?

Answer 1

I assume that E and F are both 2 x 2. For example, E has first row [2 -1] and second row [3 0].

E and F are inverses as long as EF = FE = the 2 x 2 identity matrix.

This is not true, since EF is 2 x 2 with first row [1 0] and second row [0 3].

Note: the inverse of E has first row [0 1/3] and second row [-1 2/3]

Answer 2

A row or column vector does not have an inverse. The requirement is for the domain and range of your linear operator to be the same space.