GATE 2024 CS (CS2) – Question 63
Let $Z_n$ be the group of integers $\{0,1,2,\ldots,n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_2\times Z_3\times Z_4$ that are their own inverses is ________
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Correct answer: 4
Explanation
An element is self-inverse iff 2x = 0 in every coordinate: Z2 has 2 such elements, Z3 has 1 (only 0), Z4 has 2 (0 and 2). Total = 2×1×2 = 4.