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Prove that if an m x m matrix A is upper-triangular, then A-1 is also upper-triangular....

Prove that if an m x m matrix A is upper-triangular, then A-1 is also upper-triangular.

Hint: Obtain Axj=ej where xj is the jth column of A-1 and ej is the jth column of I. Then use back substitution to argue that xij = 0 for i > j.

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