Mathematics · Abstract Algebra
Let R be the set of all 2 × 2 real matrices with trace zero, i.e., R = { [ abcd ] : a, b, c, d ∈ ℝ, a + d = 0 }. Under standard matrix addition and multiplication, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(R, +, ·) is not closed under matrix multiplication, hence it is not a ring.✓
- 2(R, +, ·) is a ring with identity.
- 3(R, ·) is a group, but (R, +, ·) is not a ring.
- 4(R, +) is a group, but (R, +, ·) is not a ring.
Correct answer
(R, +, ·) is not closed under matrix multiplication, hence it is not a ring.
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