# Proving linear algebra

annoymage
let A € M(2x2)..
if AB=BA for all B(2x2),
show that A=àI for all à € real number

its really hard to send new post using phone..

Homework Helper
Do you understand the question? Basically, it's asking you to prove that the only matrix that commutes with any other matrix is the identity matrix.

Well, if you don't see any clever way to solve it (like me at first reading), you could simply take two matrices,

$$A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}, \qquad B = \begin{pmatrix} x & y \\ u & v \end{pmatrix}$$
and see what equations you get when you multiply AB = BA. Then note that this equations should hold for any values of x, y, u and v - allowing you to solve for a, b, c and d.

annoymage
before that,its hard to give my answer, so please teach me how to make that latex matrix.