Re: Linear algebra, matrices, and you
 

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If you regard all n-vectors as n x 1 matrices, then the dot product of two vectors, x and y, is just the matrix product, x^T y. This fact might be helpful.

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if you can't get it from this...

Re: Linear algebra, matrices, and you
 

in case noone has answered yet:

1) True: x.x is the length of the vector squared.

2) False: set all entries in C =0, A and B can then be any two matricies.

3)True: A=AI=ACB=IB=B

4) True: I assume by square you mean no. of rows = no. of columns, if so this is really obvious

Bonus:

(Ax) . (Ay) = (Ax)T (Ay) = xT AT A y = xT I y = xT y= x . y