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) A^2B^3 = B^3A^2
b) A^2B^3 = B^2A^3
c) A^2B^3 = BA^4
d) None of the above

1 Answer
May 27, 2018

= B^3A ^2

Explanation:

AB = - BA

A^2B^3 = A (A B) B B

= A (-B A) B B

= -(A B) (A B) B

=- BA (BA) B

=- B(A B)(A B)

=- B(BA)(BA)

= -BB(AB)A

= BB(BA)A

= B^3A ^2