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Let A = N x N and * be a binary operation on A defined by (a,b)*(c,d)=(ac,bd), show that : (i) (A*) is commutative. (ii) (A*) is associative (iii) Find the identity element, if any, in A.
cbse
class12
modelpaper
2012
sec-c
q23
math
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asked
Jan 31, 2013
by
thanvigandhi_1
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1 Answer
Let A = N x N and * be a binary operation on A defined by (a,b)*(c,d)=(ac,bd), show that : (i) (A*) is commutative. (ii) (A*) is associative (iii) Find the identity element, if any, in A.
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Jul 8
by
s.kpandey26
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Related questions
Let * be binary operation of N x N defined by (a,b)*(c,d)=(a+c,b+d). Show that * is commutative as well as associative. Find the identity element for the operation * on N x N, if any.
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Feb 2, 2013
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Let * be binary operation of N x N defined by (a,b)*(c,d)=(a+c, b+d). Show that * is commutative as well as associative. Find the identity element for the operation * on N x N, if any.
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Let $(A=N \times N \,and\, * )$ be the binary operation on $(A)$ defined by $( (a, b) * (c, d) = (a + c, b + d))$. Show that * is commutative and associative. Find the identity element for * on $( A )$, if any.
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Let * be binary operation on Q defined by $ a*b=\large\frac{3ab}{5} $ show that * is commutative as well as associative. Also find its identity element if it exists.
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Let * be the binary operation on N given by p * q = LCM of p and q. Find (i) 12 * 56 (ii) whether * is commutative? (iii) whether * is associative (iv) identity of * in N.
cbse
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Jan 15, 2013
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Let \(\ast\) be the binary operation on \(N\) given by \(a\ast b=L.C.M\,.of\,a\,and\,b\). Find $\begin{array}{1 1}(i)\;\; 5 \ast7,\; 20 \ast 16 & (ii)\;\; Is\; \ast \;commutative?\\(iii)\;\; Is\; \ast \;associative? & (iv)\;\; Find\, the\,identity \, of \ast \, in N\\(v)\;\; Which \, elements\, of \, N\, are\, invertible\, for\, the\, operaation\,\ast ? & \;\end{array}$
cbse
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asked
Nov 21, 2012
by
vaishali.a
2
answers
On the set $R -\{ -1\} $ a binary operation $\ast$ is defined by $a \ast b = a + b + ab$ for all $a,b \in R - \{-1\}$. Prove that $\ast$ is commutative as well as associative on $R -\{-1\}$. Find the identity element on $\ast$ if any.
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Dec 21, 2016
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priyanka.c
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