$(\lambda +1) (\lambda -1)(\lambda +2)(\lambda -2)=0$
$=>(\lambda ^{2}-1) (\lambda ^{2}-4)=0$
$=>\lambda ^{4} -5\lambda ^{2} +4=0$
$=> A^{4}-5A^{2}+4=0$
So, B= I So eigen values of identity matrix B are 1,1,1,1 and det(B)=1. option B is correct.
option A is also correct because on adding A and B and then after finding product of diagonals of A+B we will get 0.
option C is also true.
Answer : D