If A = {-1, 1}, then `A xx A` is equal to

Options

A. {(-1, 1), (1, -1)}
B. {(-1, -1), (1, 1)}
C. {(-1, -1), (-1, 1), (1, -1), (1,1)}
D. {(-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (-1, 1, 1), (1, -1, -1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}

Answer

To find the Cartesian product \( A \times A \) where \( A = \{-1, 1\} \), we will follow these steps:

### Step 1: Understand the Cartesian Product
The Cartesian product \( A \times A \) is defined as the set of all ordered pairs \( (a, b) \) where \( a \) and \( b \) are elements of set \( A \).

### Step 2: List the Elements of Set A
The elements of set \( A \) are:
- \( -1 \)
- \( 1 \)

### Step 3: Form Ordered Pairs
Now, we will form all possible ordered pairs \( (a, b) \) where \( a \) and \( b \) can each be either \( -1 \) or \( 1 \).

1. Pairing \( -1 \) with \( -1 \): \( (-1, -1) \)
2. Pairing \( -1 \) with \( 1 \): \( (-1, 1) \)
3. Pairing \( 1 \) with \( -1 \): \( (1, -1) \)
4. Pairing \( 1 \) with \( 1 \): \( (1, 1) \)

### Step 4: Write the Cartesian Product
Now, we can write the Cartesian product \( A \times A \):
\[ A \times A = \{ (-1, -1), (-1, 1), (1, -1), (1, 1) \} \]

### Final Answer
Thus, the Cartesian product \( A \times A \) is:
\[ \{ (-1, -1), (-1, 1), (1, -1), (1, 1) \} \]

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