Science:Math Exam Resources/Courses/MATH221/December 2019/Question 04 (c)/Statement

In each of the following, indicate the correct answer (and only the correct answer) by circling the appropriate letter. You do not have to show your work in this question.

Consider the following statements about an $n\times n$ matrix $A$:

1. If the map ${\bf {x}}\mapsto A{\bf {x}}$ is one-to-one then it is also onto $\mathbb {R} ^{n}$.

2. If the map ${\bf {x}}\mapsto A{\bf {x}}$ is onto $\mathbb {R} ^{n}$ then it is also one-to-one.

Which of the statements above are true?

A: Both statements are true

B: Only statement 1 is true

C: Only statement 2 is true

D: Both statements are false