If A = [1 cot x; –cot x 1], show that A′A⁻¹ = [–cos 2x –sin 2x; sin 2x –cos 2x].

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TextDeterminant of a Matrix of Order ThreeInverse of a Square Matrix Using AdjointSolving System of Linear Equations Using Inverse of MatrixCBSE PYQ

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Assertion (A) : For matrix A = [1 cos θ 1; – cos θ 1 cos θ; – 1 – cos θ 1], where θ ∈ [0, 2π], |A| ∈ [2, 4]. Reason (R) : cos θ ∈ [– 1, 1], ∀ θ ∈ [0, 2π].

Assertion-ReasonDomain and Range of Trigonometric FunctionsDeterminant of a Matrix of Order Three

If A = [1 –2 0; 2 –1 –1; 0 –2 1], find A⁻¹ and use it to solve the following system of equations : x – 2y = 10, 2x – y – z = 8, – 2y + z = 7

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