Consider the following statements
I. A matrix is not a number.
II. Two determinants of different orders may have the same value.
Which of the above statement(s) is/are correct ?

Options

A. A. Only I
B. B. Only II
C. C. Both I and II
D. D. Neither I nor II

Answer

To solve the question regarding the correctness of the statements about matrices and determinants, let's analyze each statement step by step.

### Step 1: Analyze the First Statement
**Statement I:** A matrix is not a number.

- A matrix is defined as an ordered rectangular array of numbers. It consists of rows and columns filled with numerical values.
- Since a matrix is a collection of numbers arranged in a specific format (like a table), it cannot be classified as a single number.

**Conclusion for Statement I:** This statement is **correct**.

### Step 2: Analyze the Second Statement
**Statement II:** Two determinants of different orders may have the same value.

- To understand this, we need to consider determinants of different orders (sizes).
- Let's take an example of a 2x2 determinant:
\[ \begin{vmatrix} 2 & 5 \\ 1 & 4 \end{vmatrix} \]
The determinant is calculated as:
\[ (2 \times 4) - (5 \times 1) = 8 - 5 = 3 \]

- Now, let's consider a 3x3 determinant:
\[ \begin{vmatrix} 1 & 3 & 0 \\ 3 & 0 & 2 \\ 2 & 0 & 1 \end{vmatrix} \]
The determinant can be calculated using the rule of Sarrus or cofactor expansion. After calculating, we find that the value of this determinant is also 3.

**Conclusion for Statement II:** This statement is also **correct**.

### Final Conclusion
Both statements are correct. Therefore, the answer is that both Statement I and Statement II are correct.

### Final Answer
Both statements are correct.

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