DeterminantHard
Question
Find number of all possible ordered sets of two (n × n) matrices A and B for which AB - BA = I
Options
A.infinite
B.n2
C.n!
D.zero
Solution
Assume C = AB - BA
If C = I
then trace (C) = 1 + 1 + ........ + 1 = n
But trace (C) = 0 (∵ trace (AB) = trace (.BA) )
Which is a contradiction
Hence no such ordered pair is possible.
If C = I
then trace (C) = 1 + 1 + ........ + 1 = n
But trace (C) = 0 (∵ trace (AB) = trace (.BA) )
Which is a contradiction
Hence no such ordered pair is possible.
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