If A = [ c o s α s i n α − s i n α c o s α ] , then A 2 = Options: A . &nbsp[cos2αsin2αsin2αcos2α] B . &nbsp[cos2α−sin2αsin2αcos2α] C . &nbsp[cos2αsin2α−sin2αcos2α] D . &nbsp[−cos2αsin2α−sin2α−cos2α]

Answer: Option C : C Since A 2 = A . A = [ c o s α s i n α − s i n α c o s α ] [ c o s α s i n α − s i n α c o s α ] = [ c o s 2 α s i n 2 α − s i n 2 α c o s 2 α ] .

If A=[cosαsinα−sinαcosα], then A2=

Question

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

, then

A^{2} =

Options:

A . [cos2αsin2αsin2αcos2α]

B . [cos2α−sin2αsin2αcos2α]

C . [cos2αsin2α−sin2αcos2α]

D . [−cos2αsin2α−sin2α−cos2α]

Answer: Option C
:
C
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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