Icos lalpha - sin- Isin - cos lalphalendbmatrix - then - AA - A- AB- Zero matrixC- A -D- I

The correct option is D IAA'=[ nbsp;cosα nbsp; amp; sinα; sinα nbsp; amp; cosα ][ nbsp;cosα nbsp; amp; sinα; sin ...

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Standard XII

Mathematics

Algebra of Derivatives

Icos lalpha &...

Question

$If A = [\begin{matrix} cos α & sin α - sin α & cos α \end{matrix}], then A A^{'} =$

A

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Zero matrix

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A^{'}

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I

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Solution

The correct option is D $I$
$A A^{'} = [\begin{matrix} cos α & sin α - sin α & cos α \end{matrix}] [\begin{matrix} cos α & - sin α sin α & cos α \end{matrix}]$

$= [\begin{matrix} {cos}^{2} α + {sin}^{2} α & 0 0 & {cos}^{2} α + {sin}^{2} α \end{matrix}]$

$= [\begin{matrix} 1 & 0 0 & 1 \end{matrix}] = I$

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If A=[cosαsinα−sinαcosα],then AA′=

The correct option is D IAA′=[cosαsinα−sinαcosα][cosα−sinαsinαcosα] =[cos2α+sin2α00cos2α+sin2α] =[1001]=I

$If A = [\begin{matrix} cos α & sin α - sin α & cos α \end{matrix}], then A A^{'} =$