Chapter 9.2, Problem 70E

a.

To determine

To check: Whether the system is closed or not under multiplication for the single element $\left\{1\right\}$.

b.

To determine

To check: Whether the system having identity element or not under multiplication for the single element $\left\{1\right\}$.

c.

To determine

To check: Whether 1 have multiplicative inverse or not for the single element $\left\{1\right\}$.

d.

To determine

To check: Whether the system holds associative property or not under multiplication for the single element $\left\{1\right\}$.

e.

To determine

To check: Whether the system holds commutative property or not under multiplication for the single element $\left\{1\right\}$.

f.

To determine

To check: The singleton set $\left\{1\right\}$ is commutative group under multiplication.