Correct Answer - Option :

__Answer__: Option 2 and Option 3

**Concept**:

**Injection**:

It is Mapping/function between two sets A and B (f: A→ B) such that every element in A mapped to a unique element in B. ( one-one function )

**Surjection**:

It is Mapping/function between two sets A and B **(f: A→ B)** such that every element in B has a pre-image in A.(onto Function).

**Bijection**:

It is Mapping/function between two sets A and B such that every element in A is mapped to exactly one element in B and every element in B has an exactly one pre-image in A.

__Explanation__:

**S**_{1}: Set of all n x n matrices with entries from the set {a, b, c}

So in an n× n Matrix total number of the position will be n^{2} and these positions can be filled from any element from the set { a, b, c}

Hence the total number of matrices possible = \({3^{{n^2}}}\)

**S**_{2}:Set of all functions from the set {0,1, 2, ..., n2 — 1} to the set {0,1,2}

number of all functions in S_{2} will be \({3^{{n^2}}}\).

**Option 1**:There does not exist an injection from S1 to S2.

This is **not correct**. Since the cardinality of both the sets S_{1} and S_{2} is equal. So we can draw one-to-one mapping between Set S_{1} and S_{2}.

**Option 2**: There exists a bijection from S1 to S_{2}.

This is __correct__. Since the cardinality of both the sets S1 and S2 is equal. and hence Bijective function/mapping possible between Set S1 and S2.

__Option 3__: There exists a surjection from S1 to S2.

This is **correct**. Since Bijection possible and hence Surjection also possible. Bijection implies Surjection but not vice versa.

__Option 4__:There does not exist a bijection from S1 to S_{2}.

This is **not correct.**