Suppose A & B are square matrices that satisfy AB+BA=0, where 0 is the square matrix of 0's. Then which of the following holds?

a) A2B3=B3A2
b) A2B3=B2A3
c) A2B3=BA4
d) None of the above

1 Answer
May 27, 2018

=B3A2

Explanation:

AB=BA

A2B3=A(AB)BB

=A(BA)BB

=(AB)(AB)B

=BA(BA)B

=B(AB)(AB)

=B(BA)(BA)

=BB(AB)A

=BB(BA)A

=B3A2