# Inverse of a fundamental matrix

1. Dec 31, 2007

### Diferencialdex

Hello, I have a little problem. I´ve calculated the fundamental matrix of a EDO system, such that:

M(t) = P * exp( J*t)

where J is a diagonal matrix:

J = [-3 , 0 ; 0 , 1] and P = [1 , 1 ; 3 , -3]

The problem arise when I try to find the inverse matrix of M. What I do is this

As we know the inverse of a product is the product of the inverse, so firstly I find P$$^{-1}$$. Then I look for the inverse of exp(J*t), that in this case is exp( -J*t). That´s all. Now, when I do the product of the two inverse matrix, the result is not the resul of the inverse of M. Can anyone tell me where ir my mistake?

Thank you!

Last edited: Dec 31, 2007
2. Dec 31, 2007

### Rainbow Child

The right formula is

$$M=A\cdot B\Rightarrow M^{-1}=B^{-1}\cdot A^{-1}$$

Did you reverse the order of A, B?

3. Dec 31, 2007

### Diferencialdex

That was the problem . What a stupid mistake!!!

Thank you very much!!

4. Dec 31, 2007

### Rainbow Child

I am glad that I helped!