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=Null space, CS=column space) NS(EA) = NS(E) RS(EA) = RS(A) CS(EA) = C5(A) RS(EA) = CS(A) NS(A) = NS(AE) (ii) and (iii) (i) and (ii) (ii) and (iv) (i), (ii) and (v) None of the above

Solution

ii) and third are true

Since the rows of EA will be the same as A

similarily for the columns of EA