Let M be the set of all singular matr...

Let `M` be the set of all singular matrices of the form `[xxxx]` , where `x` is a non-zero real number. On `M` , let `` be an operation defined by, `AB=A B` for all `A ,\ B in Mdot` Prove that `*` is a binary operation on `Mdot`

Similar Questions

Explore conceptually related problems

On the set Z of integers a binary operation * is defined by a*b=ab+1 for all a,b in Z Prove that * is not associative on Z

Let ^(*) be a binary operation on Q-{0} defined by a*b=(ab)/(2) for all a,b in Q-{0} Prove that * is commutative on Q-{0}

Let * be a binary operation on N defined by a*b = a^(b) for all a,b in N show that * is neither commutative nor associative

Let * be the binary operation on N defined by a*b=HCF of a and b .Does there exist identity for this binary operation on N?

Let Q be the set of all rational numbers and * be the binary operation , defined by a * b=a+ab for all a, b in Q. then ,

Let * be a binary operation on Z defined by a*b=a+b-4 for all a,b in Z. show that * is both commutative and associative.

On the set Q of all rational numbers an operation * is defined by a*b=1+ab. show that * is a binary operation on Q.

:' on Q defined by a*b=(a-1)/(b+1) for all a,b in Q define a binary operation on the given set or not:

On the set W of all non-negative integers * is defined by a*b=a^(b) .Prove that * is not a binary operation on W.

Determine whether * on N defined by a*b=a^(b) for all a,b in N define a binary operation on the given set or not: