The Best Answer for Select all statements below which are true for all invertible n×n matrices A and B?
A) True, since |A| ≠ 0 implies that |A^2| = |A|^2 ≠ 0.
B) True (for any exponent instead of 7 as well).
C) False, since AB ≠ BA in general:
(A + B)^2 = (A + B)A + (A + B)B = A^2 + BA + AB + B^2.
D) False, since this is equivalent to AB = BA which is not true in general.
E) False; the actual formula is (AB)^(-1) = B^(-1) A^(-1), since
(AB)(B^(-1) A^(-1)) = A (BB^(-1)) A^(-1) = AIA^(-1) = AA^(-1) = I.
F) False; A = I and B = -I are invertible, but A + B = 0 is clearly not invertible.
I hope this helps!