# Matrix identities and determinants

• Nov 11th 2008, 03:24 PM
SuumEorum
Matrix identities and determinants
Hey there, I just wanted to confirm something, if AB=I where A and B are square matrices and I the identity matrix, can we then say that |A||B|=|I|? Thanks a lot (Hi).
• Nov 11th 2008, 03:42 PM
Hellreaver
Quote:

Originally Posted by SuumEorum
Hey there, I just wanted to confirm something, if AB=I where A and B are square matrices and I the identity matrix, can we then say that |A||B|=|I|? Thanks a lot (Hi).

From what I can tell, yes. For instance:

1 2
3 1

has an inverse of
-1/5 2/5
3/5 -1/5

The determinant of the first matrix is:
-5 ((1x1)-(2X3))
And the second is:
-1/5.

By multiplying the two, you get 1, which is det(I).
• Nov 11th 2008, 03:50 PM
whipflip15
You can do that with any matrices (not just the identity) because

$det(AB)=det(A)det(B)$
• Nov 11th 2008, 03:52 PM
SuumEorum
Aah I see, thanks :D
• Nov 11th 2008, 03:56 PM
Hellreaver
Quote:

Originally Posted by whipflip15
You can do that with any matrices (not just the identity) because

$det(AB)=det(A)det(B)$

I was going to put that in, but I wasn't 100% sure it was relevant. :D