Exercise 12:

det(2B) = (2)(2)(2) det(B) = (8)(9) = 72.
det(-B) = det ((-1)B) = (-1)(-1)(-1)det(B) = (-1)det(B) = (-1)(9) = -9.

And in general if "C" is an "n"x"n" matrix and "r" is any real number then

det(rC)= (r)(r)...(r)det(C) = (r)^(n) det(C)    here ^ = "raised to the power"
	 \----v----/
	  "n"-times


Exercise 8:

On line 4 there is a "typo"

It sould go like this:

|| x + y ||^(2) = (x + y).(x + y) = x.(x + y) + y.(x + y) = ...

compare with x.(x + y) + y(x.y) which is what I wrote.