Still ,Matrices, A is square: If AB = Identity, is B the inverse?

If In is a matrix the coefficients of which belong to a some ring, the
result is it really still? I think that yes. Can one prove him(it) without
determinant?



.

Relevant Pages

  • Re: Confirmed flaw in the polynomial ring A[X] construction
    ... different ring*. ... all the polynomials would get ... does not address the polynomial with real coefficients and the effect ... usage or construction composed with y. ...
    (sci.math)
  • Re: understanding formal objects in computer languages
    ... where r may be any type derived from Ring ... of looking up coefficients in the sequence ... many writers will skip the formality of the "marking of elements" ... polynomials so long as X is untouchable. ...
    (sci.math)
  • Re: When do we know if large sets of objects exists?
    ... the union, A, of all such sets S' exists. ... As for ring ideals, one can presumably deduce ... s does not belong to x S, and the argument can go ahead. ...
    (sci.math)
  • Re: Factorization of Anal Explosions
    ... ring of algebraic ... which are roots of monic polynomials with integer ... coefficients and a last coefficient of 1 or -1. ... so by the rule the exclusion is the result of N ...
    (sci.math)
  • Re: Understanding the quotient ring nomenclature
    ... This is a trivial implication of the fact that a ring is (by ... because multiplication of polynomials includes ... stuff that simply does not exist in the reals, ... even with a wildly different field of coefficients. ...
    (sci.math)
Loading