all questions in problem 4.3

Problem 4.3. True and False: 1. det(A + I) = det(A) + 1. 2. det(ABC) = | det A| | det B| | det C| 3. If A is invertible, then 0 is definitely not an eigenvalue. 4. For a n xn matrix A, there are always n eigenvalues (count multiplicity and allowing complex e. v . ) . 5. If a 3 x 3 matrix B has eigenvalue 0,1,2. Then rank(B) 0