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  1. If $A$ and $B$ two matrices of order $n\times n$ such that $AB=I$ then $A$ and $B$ are commutative and

  2. Give any two reasons for A and B commutative.

I know what

... one matrix is the Identity matrix.

... one matrix is the Zero matrix.

... both matrices are 2×2 rotation matrices. (basically case #2)

... both matrices are Diagonal matrices.

how to prove part one

Kenny Lau
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Inverse Problem
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  • I think you shall say that is B is a right inverse of A, then B is the inverse of A. This is an indirect consequence of the nullity-rank. – Li Chun Min May 12 '17 at 05:55
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    The rest of your question is incomprehensible to me. – Kenny Lau May 12 '17 at 05:56
  • This might be very helpful https://math.stackexchange.com/questions/236212/simultaneously-diagonalizable-proof – QED May 12 '17 at 06:05

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