(Solved): Answer Quickly for guaranteed thumbs up     8. (15 pts) Let A be an n xn matrix such tha ...

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8. (15 pts) Let A be an n xn matrix such that AT =-A and let B = 1 - A, where I is the n x n identity matrix. Let u EN(B), i.e., u is in the null space of B. (a) (2 pts) Show that Au = u. (b) (4 pts) Show that u? Au = " Au. (c) (4 pts) Using part(b), show that u = 0, i.e., u is the zero vector. (d) (Extra Credit 5 pts) Determine rank B.