# Question: please follow the comment and explain it step by step...

###### Question details

**Please follow the comment and explain it step by
step**

Let A be a 2 × 2 matrix, and let LA be the linear

operator defined by

L(x) = Ax

Show that

(a) L maps R2 onto the column space of A.

(b) if A is nonsingular, then LA maps R2 onto R2