The operation "*" is defined on R by 11ab for all a,be R. Which of the 19 following is true about the operation? a*b = A. The operation does not obey the law of the inverse. B. The operation obeys the law of inverse and the inverse of is 1 a a C. The operation obeys the law of inverse and the inverse of a is a 11 19a D. The operation obeys the law of the inverse and the inverse of 361 a ER is a -1. 121a

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question
The operation "*" is defined on R by
11ab
a*b=
for all a,be R. Which of the
19
following is true about the operation?
A. The operation does not obey the
law of the inverse.
B. The operation obeys the law of
inverse and the inverse of is
1
a
a
C. The operation obeys the law of
inverse and the inverse of a is
a
11
19a
D. The operation obeys the law of
the inverse and the inverse of
361
a ER is a ¹-
121a
Transcribed Image Text:The operation "*" is defined on R by 11ab a*b= for all a,be R. Which of the 19 following is true about the operation? A. The operation does not obey the law of the inverse. B. The operation obeys the law of inverse and the inverse of is 1 a a C. The operation obeys the law of inverse and the inverse of a is a 11 19a D. The operation obeys the law of the inverse and the inverse of 361 a ER is a ¹- 121a
Expert Solution
Step 1

Let us consider binary operation * on G.

The identity of the G is a*e=a, aG. The identity must be unique.

The inverse of the a is b if  a*b=e, a,bG. The inverse  must be unique.

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