Det(A)= product of eigen values = 4.
Det (B)= det(A^4) -5^4 det(A^2) + 5^4 = -9119
Option B and D is eliminated.
trace(A+ B)=trace(A) + trace (B)
Trace of any matrix is equal to the sum of the eigen values . So, trace(A)= 0 and trace (B)=4 So , 0+4=4;
C is ans.