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) = CS(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

An elementary matrix E is invertible.

So multiplying by E does not affect the kernel and the range.

So (ii) and (iii) are always true.