dse 2011

[ritu]

q26...suppose A n B are square matrix that satisfy AB+BA=0
then it must be that
a.A^2B^3=B^3A^2
b q26...suppose A n B are square matrix that satisfy AB+BA=0
then it must be that
a.A^2B^3=B^3A^2
b.A ^2 B^3=B sq A cube
c.A sq B cube = B A raise to poer 4
d.none is necessarily true

[Amit Goyal]

Given AB + BA = 0, or AB = -BA.

I will just replace the AB in bold by -BA in steps below:
AABBB
= AABBB = -ABABB
= -ABABB = -BABAB
= -BABAB = -BBABA
= -BBABA = BBBAA
= BBBAA

[ritu]

omg sir!!!
that was amazing....thank u so much:-)

[Amit Goyal]

Most welcome mam :-)