#matrix

Question

Let A be a 4 × 4 matrix with real entries such that -1, 1, 2, -2 are its eigen values. If B = A⁴ - 5A² + 5I where I denotes 4 × 4 identity matrix, then which of the following is correct? (det(X) represents determinant of X)

(A) det(A + B) = 0
(B) det(B) = 1
(C) trace of A + B is 4
(D) all of these

Comments

Thank You so much joshi_nitish Sir and  Anu007 Sir .. 

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@nitish good explanation!

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Is A Matrix is also a diagonal matrix?

Because if A is not diagonal matrix then following calculation will be wrong

DET(A+B) = {-1+1,1+1,-2+1,2+1}={0,2,-1,3} =0

So please tell me how identify matrix A is diagonal Matrix.