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Identity Satisfaction (Posted on 2014-08-05) Difficulty: 3 of 5
Each of A and B is a real nxn matrix with:
  • A+B = I (identity) and:
  • rank(A)+rank(B) = n
Does each of those identities always hold?
  1. A2 = A
  2. B2 = B
  3. AB = BA = 0
If so, prove it.
Otherwise, provide a counterexample.

No Solution Yet Submitted by K Sengupta    
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  Subject Author Date
SolutionSome Linear AlgebraBrian Smith2016-02-03 11:57:22
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