Question: A square matrix is upper triangular if each i, j entry is zero in the part above the diagonal, that is, when i > j.

A square matrix is upper triangular if each i, j entry is zero in the part above the diagonal, that is, when i > j.
(a) Must the adjoint of an upper triangular matrix be upper triangular? Lower triangular?
(b) Prove that the inverse of a upper triangular matrix is upper triangular, if an inverse exists.

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