Please I need you to check my answer and see if I did it cor

Please I need you to check my answer and see if I did it correctly or not. Also, I need you to give me your advice to improve my answer.

Thanks...

2 n, show that A A is nonsingular if and (15pts) Given A ERmxn, with m only if A has full rank.

Your solution is absolutely clear , and precise. It is therefore correct too .

No improvement needed to improve the solution of this question

Alternatively you can do it in ways which can make the process shorter , like only proving the converse

A has full rank if A^TA is invertible.