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Unformatted text preview: -6-7 2-3 2 6 3 2-1-1 2-1 2 . 2. (a) is false. For example, if A = I and B =-I , then both A and B are invertible, but A + B = 0, which is not invertible. (b) is true. Suppose A 2 is invertible and has inverse matrix B . Then A 2 B = I , by deﬁnition. Hence A ( AB ) = I . Therefore, A is invertible and has inverse AB . (c) is false. For example, if L A and L B happen to be the same line, then AB is the result of reﬂecting twice across the same line, which is just the identity transformation. The identity transformation certainly is not a reﬂection across any line. (More generally, the 1 product of two reﬂections will be a rotation; see problem 42 in section 2.4 of the Bretscher text.) 2...
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This note was uploaded on 04/02/2008 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.
- Fall '08