- 2 Let M Denote The Set Of All 2 2 Matrices Over R Recall That Product Of Matrices Gives A Binary Operation On M Whic 1 (83.06 KiB) Viewed 41 times
2. Let M denote the set of all 2 × 2 matrices over R. Recall that product of matrices gives a binary operation on M whic
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2. Let M denote the set of all 2 × 2 matrices over R. Recall that product of matrices gives a binary operation on M whic
2. Let M denote the set of all 2 × 2 matrices over R. Recall that product of matrices gives a binary operation on M which is associative and unital (the identity matrix is (9)). (i) Let GM be the set of 2 × 2 matrices whose determinant is non-zero. Show that a product of two matrices in G is a matrix in G, thus matrix multiplication gives a well defined binary operation on G. Show that matrix multiplication makes G a group. Why is M not a group under this operation? [3 marks] (ii) Let N M be the set of 2 x 2 matrices whose determinant is equal to 1. Show that N is a normal subgroup of G. Show that G/N RX. [3 marks]
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