Consider the following statements in respect of the square matrices A and B of same order:
1. A and B are non-zero and AB = 0 `rarr` either |A| = 0 or |B| = 0
2. `AB = 0 rarr A = 0 or B = 0`
Which of the above statements is/are correct ?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Explanation

To solve the problem, we need to analyze the two statements regarding the square matrices \( A \) and \( B \) of the same order.

### Step 1: Analyze the second statement
The second statement claims:
\[ AB = 0 \Rightarrow A = 0 \text{ or } B = 0 \]

To evaluate this, we can consider a counterexample. Let:
\[ A = \begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}, \quad B = \begin{pmatrix} 0 & 0 \\ 3 & 4 \end{pmatrix} \]

Calculating the product:
\[ AB = \begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix} \begin{pmatrix} 0 & 0 \\ 3 & 4 \end{pmatrix} = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \]

Here, \( AB = 0 \) but neither \( A \) nor \( B \) is the zero matrix. Therefore, the second statement is **not correct**.

### Step 2: Analyze the first statement
The first statement claims:
\[ AB = 0 \Rightarrow |A| = 0 \text{ or } |B| = 0 \]

Using the property of determinants, we know:
\[ |AB| = |A| \cdot |B| \]
If \( AB = 0 \), then:
\[ |AB| = |0| = 0 \]
This implies:
\[ |A| \cdot |B| = 0 \]
For the product of two determinants to be zero, at least one of the determinants must be zero. Thus, we conclude:
\[ |A| = 0 \text{ or } |B| = 0 \]
Therefore, the first statement is **correct**.

### Conclusion
- The first statement is correct.
- The second statement is incorrect.

Thus, the answer is that only the first statement is correct.

### Final Answer
**Option A: 1 only**

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