If A - begin bmatrix cos lalpha - sin lalphall-sin lalpha - cos lalpha lend bmatrix - then A 2-A- Vbeginbmatrix cos 2 - sin 2 lalphallsin 2 lalpha - cos 2 lalpha e n d b m a t r i x B- cos 2 - - sin 2 lalphallsin 2 - cos 2 lalpha e n d b m a t r i x cos 2 - sin 2 lalphall- sin 2 lalpha - cos 2 lalpha endbmatrix - cos 2 - sin 2 lalphall- sin 2 lalpha - - cos 2 lalpha e n d b m a t r i x

The correct option is C [ cos 2 α amp; sin 2 α; sin 2 α amp; cos 2 α ]SinceA^2 = A.A = [ cos α amp; sin α; sin α amp; cos α ][ cos α a ...

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Byju's Answer

Standard X

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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