Show that `(Z_7-{[0]],.7)` write to the binary operation multification module7 satisfies closure, associative, identify and inverse properties.

Show that the set G={a+bsqrt2//a,binQ} is an infinite abelian group with respect to Binary operation addition. Satisfies closure, associative, identity and inverse properties.

Show that the set {[1].[3],[4],[5],[9]}under multiplication modulo 11 satisfies closure, associative, identity and inverse properties.

Show that the set G of all rational numbers except -1 satisfies closure, associative, identify and inverse property with respect to the operation ** given by a**b=a+b+ab for all a, b in G .

Let M={[{:(,x,x),(,x,x):}}: x in R-{0}} and let * be the matrix multiplication. Determine whether M is closed under *. If so, examine the existence of identify, existence of inverse properties for the operation * on M.

Show that the equation 3x^2-x+7=0 can not be satisfied by any real values of x.

In each of the find the equations of the hyperbola satisfying the given conditions. Vertices (+-7,0) , e=(4)/(3) .

Verify (i) closure property (ii) commutative property (iii) associative property (iv) existence of identity and (v) existence of inverse for the operation xx_(11) on a subset A = {1,3,4,5,9} of the set of remainders {0,1,2,3,4,5,6,7,8,9,10}.

The operation ** defined by a ** b =(ab)/7 is not a binary operation on

Verify (i) closure property (ii) commutative property (iii) associative property (iv) existence of identity and (v) existence of inverse for the operation +_(5) on ZZ_5 using table corresponding to addition modulo 5.