Let E be an n times n elementary matrix and A be an n times

Let E be an n times n elementary matrix and A be an n times n matrix. Which of the following statements are ALWAYS true? (RS=row space, NS=Nullspace, CS=column space) (i) NS(EA) = NS(E) (ii) RS(EA) = RS(A) (iii) CS(EA) = CS(A) (iv) RS(EA^t) = CS(A) (v) NS(A) = NS(AE) (ii) and (iii) (i) and (ii) (ii) and (iv) (i), (ii) and (v) None of the above

Solution

(ii),(iv) are the correct statements.

hence answer is C.