Part CCSIR NET December 2024each-determinant-is-raised-to-the-dimension

Each determinant is raised to the dimension

Let $M_{2} (R)$ denote the $R -$ vector space of 2 × 2 matrices with real entries. Let A = [[1, 2], [0, 3]] and B = [[−1, 0], [1, 5]]. Define a linear transformation $T : M_{2} (R) \to M_{2} (R)$ by T(X) = AXBᵗ, where Bᵗ denotes the transpose of the matrix B. Which of the following statements are true?

A.det(T) = 225✓
B.det(T) = −225
C.Trace(T) = 16✓
D.Trace(T) = −16

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: AB = I ⇒ BA = I for all matrices

Each determinant is raised to the dimension

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