If A, B and C are three sqare matrices of the same order such that A = B + C, then det A is equal to

Options

A. det A + det B
B. det B
C. det (A)
D. det (B + C)

Answer

To solve the problem, we need to find the determinant of matrix A given that \( A = B + C \), where A, B, and C are square matrices of the same order.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We are given that \( A = B + C \). This means that matrix A is the sum of matrices B and C.

**Hint**: Remember that the determinant of a sum of matrices is not equal to the sum of their determinants.

2. **Applying the Determinant Property**:
The determinant of a matrix sum does not have a simple additive property like the determinant of individual matrices. Specifically, we cannot say \( \det(A) = \det(B) + \det(C) \).

**Hint**: Recall that \( \det(A) \) is not equal to \( \det(B) + \det(C) \).

3. **Conclusion**:
Since we cannot express \( \det(A) \) in terms of \( \det(B) \) and \( \det(C) \) using simple addition, we conclude that \( \det(A) \) can be expressed as \( \det(B + C) \). However, without specific values or additional properties of matrices B and C, we cannot simplify further.

Therefore, the answer is:
\[ \det(A) = \det(B + C) \]

### Final Answer:
\[ \det(A) = \det(B + C) \]