madeeasy workbook

Question

how option a is correct

Comments

just Solve (lambda-1)(lambda+1)(lambda-2))(lambda+2)=0

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options (B) and (C) are correct, so possible answer is (D). but can someone please prove option (A) to be true

Answer 1

(A-1)*(A+1)*(A-2)*(A+2)= A4-5A2+4=0

A4-5A2=-4I

B=I=Identity matrix,

Trace of A+B= sum of eigen values of A+Sum of matrix B=-2+2-1+1+4=0