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GATE 2024 MA – Question 29

Algebra · Fields and Extensions · 1 mark · Numerical answer

Find |GL₂(F₃)|, the number of invertible 2×2 matrices over the three-element field (integer).

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Correct answer: 48 to 48

Explanation

Choose the first column nonzero in 3²−1=8 ways. The second must lie outside its one-dimensional span, excluding 3 vectors from 9, leaving 6. Total **8×6=48**.

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