2025 · Paper 1 · Mathematics
Question 4
The printed question, the official key, and each model’s JSON answer plus the reasoning it wrote.
MathematicsPaper 1Single correct
Q04
Official C
Model answers
Claude Fable 5.1
Anthropic
Correct3 / 3
C
Claude Fable 5.1 reasoning
Q must be orthogonal with integer entries, so Q is a signed permutation matrix. PQ = QP requires Q to preserve the eigenspaces of P: the eigenspace for eigenvalue 2 is span{e1, e2} and for eigenvalue 3 is span{e3}. So Q is block diagonal: a 2×2 signed permutation matrix (8 choices) and a 1×1 entry ±1 (2 choices). Total = 8 × 2 = 16.
GPT 6 Astra
OpenAI
Correct3 / 3
C
GPT 6 Astra reasoning
No written reasoning was returned for this item.
GPT 5.6 Luna
OpenAI
Correct3 / 3
C
GPT 5.6 Luna reasoning
No written reasoning was returned for this item.