The identify element of `{({:(x,x),(x,x):})} x in R, x ne 0}` under matrix multiplication is

The identity element in the group M={((x,x),(x,x))|x in R, x ne 0|} with respect to matrix multiplication is..

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

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 commutative and associative properties satisfied by * on M.

The function f(x)=x-(1)/(x), x in R, x ne 0 is

The set of matrices S = {[{:( x , -x) , (-x , x):}]0 ne x in R} forms a group under multiplication operation with identify element

The function f(x)=(7)/(x)-3, x in R, x ne 0 is

Square matrices of the type [(x,x),(x,x)] form a group under the usual matrix multiplication. The identity of this group is

(x^(2) +1)/x, x ne 0

The function f(x) = x-1/x, x in R, x ne 0 is increasing

The maximum value of f(x) =(log x)/(x) (x ne 0, x ne 1) is