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Mathematics
Mathematics
Problem
If two non-zero
2
×
2
2\times 2
2
×
2
matrices
A
A
A
and
B
B
B
satisfy
A
B
=
O
2
×
2
AB=O_{2\times 2}
A
B
=
O
2
×
2
, is it necessary that
B
A
=
O
2
×
2
BA=O_{2\times 2}
B
A
=
O
2
×
2
? Give a brief reason for your answer.
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