What is your sequence of answers?
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 all A and B invertible n×n matrices?
1. AB=I does not imply that BA=I.
2. The columns of B span Rn.
3. B can have two identical rows.
4. The homogeneous system Bv=0 has only the trivial solution.
5. The matrix AT is 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!
Some of the statements are unclear to me.
Let me start with 1.
AB=I does not imply that BA=I. Since A is invertible inv(A)AB = inv(A)I or B = inv(A). Which means that A inv(A)=I does not imply that inv(A) A=I. The first statement is thus false.
I think you should reconsider your answers. The binomial inverse theorem may help. Binomial inverse theorem - Wikipedia, the free encyclopedia