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If A( )={bmatrix} &i & {bmatrix}, then

Question

If $A (θ) = [sin θ i cos θ i cos θ sin θ]$ , then

A (θ)

is invertible for all

θ \in R

A (θ)^{- 1} = A (- θ)

A (θ)^{- 1} = A (π - θ)

A (θ) + A (π + θ)

is a null matrix

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Mateo Discussed

A (θ) = [sin θ i cos θ i cos θ sin θ]

, then

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Text solutionVerified

A (θ) = [sin θ i cos θ i cos θ sin θ]

∣ A (θ) ∣ = 1

i.e A is a non singular matrix.

∴ A (θ)

is invertible for all

θ \in R

A (θ)^{- 1} = [sin θ - i cos θ - i cos θ sin θ] = A (π - θ)

A (θ) + A (π + θ)

[sin θ i cos θ i cos θ sin θ] + [- sin θ - i cos θ - i cos θ - sin θ] = O

Hence, options A,C and D.

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Question Text	If $A (θ) = [sin θ i cos θ i cos θ sin θ]$ , then
Answer Type	Text solution:1
Upvotes	150