If A and B are two matrices such that AB=A+B then det (AI3)=?
1 Answer
Jul 12, 2018
[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) )# 
Rejigging 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