Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Are there two matrices $A_{m\times n}$, and $B_{n\times m}$ such that $A.B=I_{m}$ and $B.A=I_{n}$ (here $m\neq n$)

share|improve this question
    
@William: See also: math.stackexchange.com/questions/17908/… –  InterestedGuest Mar 19 '11 at 22:11
add comment

1 Answer

No. This follows from the facts that $rk(AB) \leq \min(rk(A),rk(B))$, that $rk(I_n) = n$, and that for an $n \times m$ matrix $A$ we have $rk(A) \leq \min(m,n)$. Here $rk(\cdot)$ denotes the rank of a matrix.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.