If A - begin bmatrix cos lalpha - sin lalphall-sin lalpha - cos lalpha lend bmatrix - then A 2-A- beginbmatrix - cos 2 - sin 2 lalphall- sin 2 lalpha - - cos 2 lalpha lendbmatrix B- Vbeginbmatrix cos 2 - sin 2 lalphallsin 2 lalpha -cos 2 lalphalend bmatrix C- begin bmatrix cos 2 - - sin 2 lalphallsin 2 lalpha - cos 2 lalpha endbmatrix cos 2 lalpha - sin 2 lalphall- sin 2 lalpha - cos 2 lalpha endbmatrix

The correct option is D [ cos 2 α amp; sin 2 α; sin 2 α amp; cos 2 α ] Since A^2 = A.A = [ cos α amp; sin α; sin α amp; cos α ][ cos α ...

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Byju's Answer

Standard XII

Mathematics

Multiplication of Matrices

If A = begin ...

Question

If $A = [\begin{matrix} c o s α & s i n α - s i n α & c o s α \end{matrix}]$ , then $A^{2} =$

$[\begin{matrix} c o s 2 α & s i n 2 α s i n 2 α & c o s 2 α \end{matrix}]$

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$[\begin{matrix} c o s 2 α & - s i n 2 α s i n 2 α & c o s 2 α \end{matrix}]$

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$[\begin{matrix} c o s 2 α & s i n 2 α - s i n 2 α & c o s 2 α \end{matrix}]$

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$[\begin{matrix} - c o s 2 α & s i n 2 α - s i n 2 α & - c o s 2 α \end{matrix}]$

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Solution

The correct option is C
$[\begin{matrix} c o s 2 α & s i n 2 α - s i n 2 α & c o s 2 α \end{matrix}]$

Since $A^{2} = A . A = [\begin{matrix} c o s α & s i n α - s i n α & c o s α \end{matrix}] [\begin{matrix} c o s α & s i n α - s i n α & c o s α \end{matrix}] = [\begin{matrix} c o s 2 α & s i n 2 α - s i n 2 α & c o s 2 α \end{matrix}] .$

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A = [\begin{matrix} c o s α & s i n α - s i n α & c o s α \end{matrix}]

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If A=[cosαsinα−sinαcosα], then A2=

The correct option is C [cos2αsin2α−sin2αcos2α] Since A2=A.A=[cosαsinα−sinαcosα][cosαsinα−sinαcosα]=[cos2αsin2α−sin2αcos2α].

If $A = [\begin{matrix} c o s α & s i n α - s i n α & c o s α \end{matrix}]$ , then $A^{2} =$