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MMLU-Pro / 8037 / Suppose A and B are n × n matrices with real entries. Which of the follow are…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Suppose A and B are n × n matrices with real entries. Which of the follow are TRUE?
I. The trace of A^2 is nonnegative.
II. If A^2 = A, then the trace of A is nonnegative.
III. The trace of AB is the product of the traces of A and B.

category

math

options

  1. All of them
  2. I, II and III
  3. I only
  4. I and III only
  5. II, III and I
  6. III only
  7. II only
  8. I and II only
  9. II and III only
  10. None of them

src

ori_mmlu-college_mathematics

Discussion

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Source and history

upstream_id / Original problem ID
8037
task_id
8645a1eb-57a3-5e9b-85c4-44fcc4bdf418
task_key
default--test--8037
task_revision_id
1
config / split
default / test

Official source

initial import