Hi I just wanted to double check the answers for these T/F Matrix statements, hopefully they are simple to determine for you guys...

Which of the following statements are true for allAandBinvertiblen×nmatrices?

1.AB=Idoes not imply thatBA=I.

2.The columns ofBspan Rn.

3.Bcan have two identical rows.

4.The homogeneous systemBv=0has only the trivial solution.

5.The matrixATis invertible.

6.(ABA^−1)^3=AB^3A^−1

7.A^7B^5 is invertible

8.(AB)^−1=A^−1B^−1

9.A+A^−1 is invertible

10.(A+B)(A−B)=A^2−B^2

Thank you!