If <strong>ALL</strong> elements of a third order determinant are equal to 1 or -1, then the value of the determinant is:
- A. 0 <strong>ONLY</strong>
- B. an even number but <strong>NOT</strong> necessarily 0 ✓
- C. an odd number
- D. 0, 1 or -1
Correct Answer: B. an even number but <strong>NOT</strong> necessarily 0
Explanation
A 3 \times 3 determinant expands to 6 terms, each being a product of 3 elements. Each term will thus be either 1 or -1. The sum of 6 odd numbers is always an even number. Depending on the arrangement, it can be 0 or non-zero even (like \pm 4).
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