Mathematics · Group Theory
Let G1 be the group of all 2 × 2 real invertible matrices under matrix multiplication, and G2 be the group of all non-zero real numbers under multiplication. If φ : G1 → G2 is defined by φ(A) = det(A), then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1φ is an isomorphism
- 2φ is an onto homomorphism but not an isomorphism✓
- 3φ is not a homomorphism
- 4φ is a one-to-one homomorphism but not an isomorphism
Correct answer
φ is an onto homomorphism but not an isomorphism
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