If A and B are two matrices such that AB=A+B then det (A-I3)=?
[Assuming A,B are 3x3 (square) matrices]
I don't know what form you are looking for but these may provide some help.
- From the given condition:
Assuming required invertibility, ie
#bb( det(A - bbbI )= (det A)/ (det B) )#
Re-jigging the condition:
Again assuming required invertibility, ie
# bb( det (A - bbbI) = 1/(det (B- bbbI)) )#
PS: You can also use the initial condition to show that