If `Delta_1=|(1,0),(a,b)|` and `Delta_2=|(1,0),(c,d)|`, then `Delta_2Delta_1` is equal to :

Options

A. ac
B. bd
C. (b-a)(d-c)
D. None of these

Answer

To solve the given problem, we need to find the product of two determinants, \( \Delta_1 \) and \( \Delta_2 \).

### Step-by-Step Solution:

1. **Define the Determinants:**
\[ \Delta_1 = \begin{vmatrix} 1 & 0 \\ a & b \end{vmatrix} \]
\[ \Delta_2 = \begin{vmatrix} 1 & 0 \\ c & d \end{vmatrix} \]

2. **Calculate \( \Delta_1 \):**
The formula for a 2x2 determinant is given by:
\[ \begin{vmatrix} p & q \\ r & s \end{vmatrix} = ps - qr \]
Applying this to \( \Delta_1 \):
\[ \Delta_1 = (1 \cdot b) - (0 \cdot a) = b - 0 = b \]

3. **Calculate \( \Delta_2 \):**
Similarly, we calculate \( \Delta_2 \):
\[ \Delta_2 = (1 \cdot d) - (0 \cdot c) = d - 0 = d \]

4. **Find the Product \( \Delta_2 \Delta_1 \):**
Now, we multiply the two determinants:
\[ \Delta_2 \Delta_1 = d \cdot b = bd \]

5. **Final Result:**
Therefore, the product \( \Delta_2 \Delta_1 \) is:
\[ \Delta_2 \Delta_1 = bd \]

### Conclusion:
The answer to the problem is \( bd \).

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