Matrices and Determinants: Mixed MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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MixedHardQuestion 250020

Question

The inverse of [[cos θ, sin θ], [−sin θ, cos θ]] is:

A
[[cos θ, −sin θ], [sin θ, cos θ]]
Correct
B
[[cos θ, sin θ], [−sin θ, −cos θ]]
C
[[−cos θ, sin θ], [−sin θ, cos θ]]
D
Same matrix

Correct answer

[[cos θ, −sin θ], [sin θ, cos θ]]

Explanation

This is a rotation matrix R(θ). Its determinant = cos²θ + sin²θ = 1. For a 2×2 matrix [[a,b],[c,d]] with det=1: inverse = [[d,−b],[−c,a]] = [[cos θ, −sin θ],[sin θ, cos θ]] = R(−θ).

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