Question

3. The following Cayley table represents the multiplication of the group G = {a, b, c, d, f} under : | a | b | c | d | f a | f | d | a | c | b b | d | a | b | f | c c | a | b | c | d | f d | c | f | d | b | a e | b | c | f | a | d (a) Find the identity of G. (b) Find the inverse of b. (c) Solve for x in the following equation: a^-1x = b.

          3. The following Cayley table represents the multiplication of the group G = {a, b, c, d, f} under *:

* | a | b | c | d | f
a | f | d | a | c | b
b | d | a | b | f | c
c | a | b | c | d | f
d | c | f | d | b | a
e | b | c | f | a | d

(a) Find the identity of G.
(b) Find the inverse of b.
(c) Solve for x in the following equation: a^-1x = b.

3. The following Cayley table represents the multiplication of the group G = a, b, c, d, f under *:

* | a | b | c | d | f
a | f | d | a | c | b
b | d | a | b | f | c
c | a | b | c | d | f
d | c | f | d | b | a
e | b | c | f | a | d

(a) Find the identity of G.
(b) Find the inverse of b.
(c) Solve for x in the following equation: a^-1x = b.

Added by Melissa R.

A Book of Abstract Algebra

Charles C. Pinter 1982 Edition

Chapter 4

Instant Answer

Solved by Expert Sri K

03/08/2023

Step 1

First, let's write down the Cayley table: $$ \begin{array}{c|cccccc} \cdot & a & b & c & d & f \\ \hline a & a & b & c & d & f \\ b & b & f & d & c & a \\ c & c & d & f & a & b \\ d & d & c & a & f & b \\ f & f & a & b & c & d \\ \end{array} $$ (a) Show more…

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The following Cayley table represents the multiplication of the group G = {a, b, c, d, f} under *: (a) Find the identity of G. (b) Find the inverse of b. (c) Solve for x in the following equation: a^-1x = b.