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    Linear Algebra: Orthogonal Bases

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    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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    Solution Summary

    This solution is comprised of an explanation of how to complete a proof regarding an orthonormal set and find the formula for the inverse of a matrix. This solution is enclosed within an attached Word document.