Example: Is det(A+B)=det(A)+det(B) , for all nn matrices A and B ? (No answer given) Counterexample: Take A=I2 and B=I2 , where I2 is the 22 identity matrix. Thus A+B= Then det(A+B)= , but det(A)+det(B)= + = Thus det(A+B) (No answer given) det(A)+det(B) in this case, and hence det(A+B) (No answer given) det(A)+det(B) in general