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 \((A - B)C = A \cdot C - B \cdot C\) is true or false, we can use the properties of matrix operations.

### Step-by-Step Solution:

1. **Understanding the Expression**: We need to analyze the left-hand side \((A - B)C\) and the right-hand side \(A \cdot C - B \cdot C\).

2. **Distributive Property of Matrices**: One of the fundamental properties of matrix multiplication is that it is distributive over addition and subtraction. This means that for any matrices \(X\), \(Y\), and \(Z\) of compatible dimensions, the following holds:
\[ (X - Y)Z = XZ - YZ \]

3. **Applying the Property**: In our case, let \(X = A\), \(Y = B\), and \(Z = C\). According to the distributive property:
\[ (A - B)C = AC - BC \]

4. **Conclusion**: Since we have shown that \((A - B)C = AC - BC\), we can conclude that:
\[ (A - B)C = A \cdot C - B \cdot C \]
Therefore, the statement is **true**.

### Final Answer:
The statement \((A - B)C = A \cdot C - B \cdot C\) is **true** because matrix multiplication is distributive over subtraction.