An n × n matrix A is said to be invertible (or nonsingular) if there is another n × n matrix B with the property that
AB = BA = In
where I n denotes the n × n identity matrix. (See Exercise 20.) The matrix B is called an inverse to the matrix A. Exercises 30–38 concern various aspects of matrices and their inverses.
(a) Show that if A is invertible, then det A 0. (In fact, the converse is also true.)
(b) Show that if A is invertible, then det(A−1)
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