Let A be an n X n matrix and, as usual, let a_1, ..., a_n denote its column vectors.
a. Suppose a_1,...,a_n form an orthonormal set. Show that A^-1 = A^T.
b. Suppose a_1,...,a_n form an orthogonal set and each is nonzero. Find the appropriate formula for A^-1.
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