Eigen value of A (-1,1,0) given. So, the eigen value of A^100 will be [ (-1)^100 , (1)^100, (0)^100 which is (1,1,0) ] hence the Eigen value of matrix --> [ A^100+ I ] = ( 1+1 , 1+1 ,0+1 ) = (2,2,1) . As it is asking for |A^100+I| = Product of it's Eigen value = ( 2*2*1 ) = 4 .