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For the ring M2(Z) described in Example 3.6. verify the associative law
of multiplication and the distributive laws. What is the zero of this ring?
Verify that the following is the identity of M2(Z). Give examples to show
that M2(Z) is a noncommutative ring.
1 0
0 1
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Solution Summary
This provides an example of verifying the associative law of multiplication and the distributive laws with respect to a ring.
Solution Preview
To verify the associative law for multiplication, we calculate the product.
( [a b] [e f] ) [r s]
( [c d] [g h] ) [t u]
=
[ae + bg ; af + bh ] [r s]
[ce + dg ; cf + dh] [t u]
=
[(ae + ...
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