How can we prove that the inverse of an upper (lower) triangular matrix is upper (lower) triangular?
Inverse of an invertible triangular matrix (either upper or lower) is triangular of the same kind
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linear-algebra
matrices
inverse
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2Why not try a constructive proof? Better yet, look at the 2-by-2 case first, and figure out how you can generalize your observations from it. – 2010-09-17
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3A further hint: look up "forward elimination" and "backsubstitution", and figure out how to use these to find the inverse of a triangular matrix. – 2010-09-17
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0Try http://www.math.lsa.umich.edu/~tfylam/Math217/proofs05-sol.pdf – 2013-12-10