If a and b are both n × n matrices of real numbers, determine if each of the following is necessarily true. that is, will the relationships always be true regardless of the specific values in a and b. prove this using the rules of matrix arithmetic as applied to a and b. do not use counter examples or specific matrices. show enough steps that it is clear why you have reached your conclusion.
(a) (a + b)^2 a^2 + 2ab + b^2
(b) aba a^2 b
(c) abab (ab)2