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A= {bmatrix} cos & -sin sin & cos {bmatrix} ,then find whic

Question

A= $[cos α s in α - s in α cos α]$ ,then find which of the following are correct
I) A is singular matrix
II) $A^{- 1}$ = $A^{T}$
III) A is symmetric matrix
IV) $A^{- 1} = - A$

only I and II

only II and III

only II

only IV

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[cos α s in α - s in α cos α]

,then find which of the following are correct
I) A is singular matrix
II)

A^{- 1}

A^{T}

III) A is symmetric matrix
IV)

A^{- 1} = - A

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Text solutionVerified

∣ A ∣ = cos^{2} α + sin^{2} α = 1

A^{T} = [cos α - sin α sin α cos α] \neq = A

A^{- 1} = \frac{1}{1} [cos α - sin α sin α cos α] \neq = - A

[A^{T} = A^{- 1}]

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Question Text	A= $[cos α s in α - s in α cos α]$ ,then find which of the following are correct I) A is singular matrix II) $A^{- 1}$ = $A^{T}$ III) A is symmetric matrix IV) $A^{- 1} = - A$
Answer Type	Text solution:1
Upvotes	150