A short quiz based on these problems will be held in
Altgeld 245 at 1pm on

Monday February 16.

(1) Define the three matrices A,B,C as follows:

Which of the fol lowing ope rations make sense? If they make
sense, what is

the result?

(a) A − 2B

(b) AB

(c) 2BA

(d) A + B

(e) A + CB.

(2) Do the following pair of matrices commute?

(3) True or false: The sum of two diagonal matrices of the
same size is a

diagonal matrix. What about their product ?

(4) Find all matrices which commute with the matrix

What about when a = b?

(5) True or false: If A and B are the same size square
matrices , then (A+B)^2 =

A^2 + 2AB + B^2.