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2022 PEA Q25

AA is 3×33 \times 3 with rank 33; BB is 3×43 \times 4 with rank 33. Then rank⁡(AB)\operatorname{rank}(AB) is

Reveal answer and solution

Answer

A

Solution

  1. 1

    AA is nonsingular (rank 33 on 3×33\times 3), hence invertible. Multiplication by an

  2. 2

    invertible matrix preserves rank: rank⁡(AB)=rank⁡(B)=3\operatorname{rank}(AB) = \operatorname{rank}(B) = 3.

Answer structure / marking notes

rank⁡(AB)≤min⁡{rank⁡(A),rank⁡(B)}\operatorname{rank}(AB) \leq \min\{\operatorname{rank}(A), \operatorname{rank}(B)\}, achieved here.

Content note

Imported from public/resources/isi/msqe/solutions/pea/2022/ISI_MSQE_PEA_2022_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.