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?

Question

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

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Answer 1 · 2018-05-27T17:15:08

#= B^3A ^2#

#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#