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The mapping ộ: (z, +)-(zn, +), defined by o(m) = m (mod n), is a homomorphism. the kerncl of this mapping is o 4z mz o nz oz the set of all real matrices of 1 p
The mapping ộ: (Z, +)-(Zn, +), defined by o(m) = m (mod n), is a homomorphism. The kerncl of this mapping is O 4Z mz O nz Oz The set of all real matrices of 1 point order 2 under multiplication O forms a group O does not form a semigroup O does not form a groupoid O forms a monoid
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Kiran goswami
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1 ans c ,nz 2 ans d
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Srinath Best Answer
The kernel of a homomorphism, is defined to be the set of those elements in the domain, which are mapped to the identity in the range of the codomain. The identity in 0, so m(mod(n)) = 0, for all m, which are multiples of n, i.e, kn. Where k is an arbitrary integer. Therefore, the answer is nZ.
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The matrices, under multiplication must have an inverse. Check whether their determinants are singular or not.
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Kiran goswami
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