lecture9 - Math 006(Lecture 9 Inverse of a Matrix Denition...

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Math 006 (Lecture 9) Inverse of a Matrix Definition 1. The identity matrix of order n is given by the following n × n matrix: 1 0 · · · 0 0 1 · · · 0 0 0 · · · 0 0 0 · · · 1 We denote the identity matrix by I . Notice that IM = MI = M for any square matrix M In general, if I is the identity of order n , then IM = M and NI = N where M is an n × m matrix and N is a p × n matrix. Definition 2. Let M be a square matrix of order n (i.e., n × n matrix) and I be the identity matrix of order n . If there exists a matrix M - 1 such that M - 1 M = MM - 1 = I, then M - 1 is called the inverse of M . Theorem 1. When M = a b c d , then M - 1 = 1 D d - b - c a where D = ad - bc , provided that D = 0 . Example 1.
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