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Table of Contents Matrices - Inverse Matrix Definition The inverse of matrix A is a matrix A -1 such that... and Note that... 1) For A to have an inverse, A must be a square (n n) matrix. 2) An inverse for A may not exist. 3) If the inverse matrix does exist, it is unique. If you have found an inverse matrix that meets the above conditions, it is the only inverse for the given matrix.

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Table of Contents Slide 2 Matrices - Inverse Matrix Definition Example 1: Show that A -1 is the inverse of A where... Since the product was the identity matrix each time, A and A -1 are inverses of each other.

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Table of Contents Slide 3 Matrices - Inverse Matrix Definition Example 2: Show that B is not the inverse of A where... Since the result of the product is not the identity, matrices A and B cannot be inverses of each other. In fact, matrix A does not have an inverse. There is no matrix that multiplied times A yields the identity.

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Table of Contents Matrices - Inverse Matrix Definition

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