Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 119684 by help last updated on 26/Oct/20

Commented by help last updated on 26/Oct/20

is the operation closed

$${is}\:{the}\:{operation}\:{closed} \\ $$

Commented by help last updated on 26/Oct/20

is it commutative  is it associative  identity of the elements  inverse of i  inverse of −1

$${is}\:{it}\:{commutative} \\ $$$${is}\:{it}\:{associative} \\ $$$${identity}\:{of}\:{the}\:{elements} \\ $$$${inverse}\:{of}\:{i} \\ $$$${inverse}\:{of}\:−\mathrm{1} \\ $$

Answered by $@y@m last updated on 26/Oct/20

Let S={−1,1,i,−i}  From operation table,  (i) a∗b∈S ∀a,b∈S  ∴ ∗ is closed.  (ii) a∗b∈b∗a ∀a,b∈S  ∴ ∗ is commutative.  (iii) Try yourself.  (iv) a∗1=a ∀a∈S  ∴ 1 is the unity element.  (iv) i∗(−i)=1  ∴ −i∈S is inverse of i  (v) Try yourself

$${Let}\:{S}=\left\{−\mathrm{1},\mathrm{1},{i},−{i}\right\} \\ $$$${From}\:{operation}\:{table}, \\ $$$$\left({i}\right)\:{a}\ast{b}\in{S}\:\forall{a},{b}\in{S} \\ $$$$\therefore\:\ast\:{is}\:{closed}. \\ $$$$\left({ii}\right)\:{a}\ast{b}\in{b}\ast{a}\:\forall{a},{b}\in{S} \\ $$$$\therefore\:\ast\:{is}\:{commutative}. \\ $$$$\left({iii}\right)\:{Try}\:{yourself}. \\ $$$$\left({iv}\right)\:{a}\ast\mathrm{1}={a}\:\forall{a}\in{S} \\ $$$$\therefore\:\mathrm{1}\:{is}\:{the}\:{unity}\:{element}. \\ $$$$\left({iv}\right)\:{i}\ast\left(−{i}\right)=\mathrm{1} \\ $$$$\therefore\:−{i}\in{S}\:{is}\:{inverse}\:{of}\:{i} \\ $$$$\left({v}\right)\:{Try}\:{yourself} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com