Determine which of the formulas hold for all invertible nxn matrices A and B
A. AB=BA
B. A^5 is invertible
C. (A+B)(A−B)=A^2−B^2
D. (AB)^−1=A^−1B^−1
E. A+B is invertible
F. (In−A)(In+A)=In−A^2
If (A - B)(A + C) = I, where I is the 66 identity matrix, and A, B and C are ANY matrices, find ALL correct statements)
A. (A - B) is invertible
B. A and B are the same size and invertible
C. (A + C) is invertible
D. A and C are the same size
E. None of the above
Determine which of the formulas hold for all invertible nn matrices A and B
A. A+B is invertible
B. ABA^−1=B
C. (A+A^−1)^7=A^7+A^−7
D. A^2B^5 is invertible
E. (In+A)(In+A^−1)=2In+A+A^−1
F. (A+B)^2=A^2+B^2+2AB
Other than that, I think that only B holds.
I am not sure about the other sets of formulas.
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