State with reason, whether the following are true of false. A, B and C are matrices of order `2 xx 2`.
(A+B).C=A.C+B.C

Answer

To determine whether the statement \((A + B) \cdot C = A \cdot C + B \cdot C\) is true or false for matrices \(A\), \(B\), and \(C\) of order \(2 \times 2\), we will analyze the expression step by step.

### Step-by-Step Solution:

1. **Identify the Expression**:
We need to evaluate the expression \((A + B) \cdot C\) and compare it to \(A \cdot C + B \cdot C\).

2. **Apply the Definition of Matrix Addition**:
The sum \(A + B\) is defined as the matrix obtained by adding corresponding elements of matrices \(A\) and \(B\).

3. **Distribute the Matrix \(C\)**:
According to the properties of matrix multiplication, we can distribute \(C\) over the sum \(A + B\):
\[ (A + B) \cdot C = A \cdot C + B \cdot C \]

4. **Conclusion**:
Since we have shown that \((A + B) \cdot C\) can be expressed as \(A \cdot C + B \cdot C\), we conclude that the statement is true.

### Final Answer:
The statement \((A + B) \cdot C = A \cdot C + B \cdot C\) is **True**.

### Reason:
The reason this statement is true is that the multiplication of matrices is distributive over addition.

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