Unformatted text preview: S is a subspace, but show your answer is correct. 4. Fix a positive integer n and dene the product of two n by n matrices ( a i,j ) and ( b i,j ) by ( a i,j ) ( b i,j ) = ( c i,j ), where c i,j = n X k =1 a i,k b k,j This product is a binary operation on M n,n called matrix multiplication and is discussed in Chapter 2, but dont appeal to the results there. (1) Show M n,n has an identity under matrix multiplication called the identity matrix . Describe the identity matrix. (2) Show that if n &gt; 1 then matrix multiplication is not commutative. (3) Assume n = 2, nd which 2 by 2 matrices have an inverse with respect to matrix multiplication, and nd the inverse under multiplication of each such matrix. 1...
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 Winter '07
 Aschbacher
 Math, Linear Algebra, Algebra, Vector Space, Ring

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