Finding the matrix inverse by diagonalisation

[Physgeek64]

How would you go about doing this, I see it so often quoted as a method, but no-where can I find an example

This is what I was thinking

D=P^(-1)AP

Would it then follow that D^(-1)=P^(-1)A^(-1)P ?

My reasoning being:

DD^(-1)= P^(-1)APP^(-1)A^(-1)P
identity matrix= P^(-1)AA^(-1)P=identity matrix

and hence

A^(-1)=PD^(-1)P^(-1)

Just wondering if this is what they meant or if I've completely missed the point

Manny thanks in advance

 

[blue_leaf77]

Yes, because finding the inverse of a diagonal matrix with all-non-zero diagonal is very easy.

 

[Physgeek64]

Yes, because finding the inverse of a diagonal matrix is very easy.

Fab - thank you. I just wanted to check :)