Unformatted text preview: S is a subspace, but show your answer is correct. 4. Fix a positive integer n and deﬁne 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 16, but don’t 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 > 1 then matrix multiplication is not commutative. (3) Assume n = 2, ﬁnd which 2 by 2 matrices have an inverse with respect to matrix multiplication, and ﬁnd the inverse under multiplication of each such matrix. 1...
View
Full Document
 Winter '07
 Aschbacher
 Math, Linear Algebra, Algebra, Vector Space, Ring

Click to edit the document details