I am confused of two things: Why is det(lambda - A) not equal to (lambda -3) -2 3 3 (lambda +4) -9 1 2 (lambda - 5) And how do you find the eigenvalues 0, 2, 2? Solution Hey to answer your second question, i would like to tell you that eigen values 0,2,2 are found by taking the determinant of[A -lambda I] to be equal to zero. That means the determinant of the matric formed with lambda (aBOVE) should be zero, on evaluation we wil get lambda =1,2,2 To answer your first question: det(lambda - A) is not equal to (lambda -3) -2 3 3 (lambda +4) -9 1 2 (lambda - 5 = this is your calculation mistake you are taking wrong cross product. Please check your calculations .