# Proving Linear System

1. Apr 11, 2010

### annoymage

1. The problem statement, all variables and given/known data

Show that there are no A,B (2x2 and real number matrices)

such that AB-BA=I2

2. Relevant equations

N/A

3. The attempt at a solution

can anyone give me clue, how to prove this?

2. Apr 11, 2010

### Gregg

Write down the full equation

$$\left( \begin{array}{cc} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array} \right)\left( \begin{array}{cc} b_{11} & b_{12} \\ b_{21} & b_{22} \end{array} \right)-\left( \begin{array}{cc} b_{11} & b_{12} \\ b_{21} & b_{22} \end{array} \right)\left( \begin{array}{cc} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array} \right)=\left( \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right)$$

After you do that it will be obvious

3. Apr 11, 2010

### annoymage

i did, but then i get,

$$\begin{pmatrix} bg-fc & af+bh+be+df \\ ce+dg-aq-ch & cf-bg \end{pmatrix}$$

assume that my

a11=a
a12=b
.
.
.
b21=g
b22=h

then? solve the equation right?

4. Apr 11, 2010

### annoymage

owh wait,

bg-fc=1

cf-bg=1

right?

5. Apr 11, 2010

### Gregg

Yeah that's the idea I think

6. Apr 11, 2010

### annoymage

hoho, that's proof alright,, thank you very much

next, can you please check my next question i posted.. ^^