試題詳解

30. Suppose A is a 3✖3 invertible matrix and I₃ is the 3✖3 identity matrix. The followings are 5 statements about A that may or may not be true.
 (1) If p(x) is the characteristic polynomial of A, then the constant term of p(x) cannot be 0.
(2) If a 3✖3 matrix B satisties AB+BA=0,then B is singular.
(3) For any 3✖5 matrix C, rank(AC)= rank( C ).
(4) If a 3✖3 matrix D is diagonalizable,then AD is also diagonalizable.

(5)If E is a 3x3 matrix and AE is singular,then E is also singular.
Which of the above statements about A is False?
(A)(1)
(B) (2)
(C)(3)
(D)(4)
(E) (5)