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 .
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 .
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).