If A = [ cos sin - sin cos ] , then

Question

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

Smart Achievers · Accepted Answer

(1)

Ans. $A^{'} A = I$

Explanation:

Given, $A = [\begin{matrix} \cos α & \sin α \\ - \sin α & \cos α \end{matrix}]$

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

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

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

$∴$ $A^{'} A = I$

Solution

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

1 $A^{'} A = I$

2 $A^{'} A = 0$

3 $A^{'} A = 2 I$

4 $A^{'} A = - I$

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Solution

Q. If A=[cosαsinα-sinαcosα], then

1 A'A=I

2 A'A=0

3 A'A=2I

4 A'A=-I