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The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
10. Let A and B be two elements of M
2
, then their product can be defined as
AB =
a
11
a
12
a
21
a
22

b
11
b
12
b
21
b
22

=
a
11
b
11
+ a
12
b
21
a
11
b
12
+ a
12
b
22
a
21
b
11
+ a
22
b
21
a
21
b
12
+ a
22
b
22

:
Is this operation commutative? Explain.
11. Consider the set
of all nonzero real numbers with division. Prove that division is neither a com-
mutative nor an associative operation on
.
Special Elements
In addition to the properties already seen, sometimes operations single out elements that have special properties.
We are all familiar with the role of 1 when using multiplication and the role of 0 when using addition. When 1
is multiplied by any number, the product is equal to the ...
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Publisher Resources

ISBN: 9780123822178