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# hw2 - entries and let G denote the set of all 2 × 2 real...

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Math 3124 Tuesday, August 30 Second Homework Due 12:30 p.m., Tuesday September 6 1. Exercise 4.2 on page 28 (2 points) 2. Page 34, Problem 5.14. Also, is this group H abelian? (3 points) 3. Recall that the transpose A 0 of the matrix A is obtained from A by interchanging the rows and columns of A . In particular, the transpose of ± a b c d ² is ± a c b d ² . Let I denote the identity 2 × 2 matrix (1’s on the main diagonal and 0’s in the two other
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Unformatted text preview: entries), and let G denote the set of all 2 × 2 real matrices A with AA = I . Prove that G is a group with respect to matrix multiplication. You may assume that matrix multiplication is associative, and also the well-known property that ( AB ) = B A for all 2 × 2 matrices A , B . (3 points) 4. Page 40, Problem 6.2. (2 points) (4 problems, 10 points altogether)...
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