It is stated in almost every linear algebra text i could find that the inverse of a triangular matrix is also triangular, but no proofs accompanied such statements.(adsbygoogle = window.adsbygoogle || []).push({});

I am convinced that it is the truth, but I have not been able to write anything down that I am satisfied with that doesnt rely on the argument that row operations on the matrix (A|I) to obtain (I|A^{-1}).

Since this would only be the forward pass(if A is lower triangular) and the backwards pass(if A is upper triangular) and these operations ultimately do not introduce non zero terms above/below the diagonal entries(depending on what A was), thus A^{-1} would be a triangular matrix of the same flavor.

Has anyone come across anything a little more elegant than simply brute forcing it?

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# Triangular matrices

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