Home › Previous year questions › GATE 2022 ES › Question 14GATE 2022 ES – Question 14 Mathematics Foundation · Linear Algebra · 1 mark · Multiple choice
P is m×n, Q is n×l, R and S are n×n. Assess I:$(PQ)^T=Q^TP^T$; II:$(RS)^{-1}=S^{-1}R^{-1}$.
Both false I true, II false Both true I false, II true Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (C) Both true
Explanation Transposition reverses multiplication order, so I holds with conformable dimensions. If R and S are invertible, $(RS)(S^{-1}R^{-1})=I$ and the reverse product is I, proving II. Thus **C**, with invertibility implicitly required by the inverse notation.
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