Question

plz solve this question

Answer 1

option 4 is the answer

Answer 2

Answer: (4)  

                    $\left[\begin{array}{ccc}cos2\alpha &sin2\alpha \\-sin2\alpha &cos2\alpha \\\end{array}\right]$

Step-by-step explanation:

Let A = $\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]$

∴ A⁻¹ = 1/|A| $\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]$          [|A| = adj.Matrix.

we know,

|A| = ad - bc

Now in our math,

$\left[\begin{array}{ccc}cos2\alpha &-sin2\alpha \\sin2\alpha &cos2\alpha \\\end{array}\right]$ = A

|A| = $cos2\alpha cos2\alpha - (-sin2\alpha sin2\alpha )$

    $= cos^{2}2\alpha + sin^{2}2\alpha$

    = 1     $[sin^{2}\alpha + cos^{2}\alpha = 1 ]$

so,

A⁻¹ = 1/1  $\left[\begin{array}{ccc}cos2\alpha &sin2\alpha \\-sin2\alpha &cos2\alpha \\\end{array}\right]$

= $\left[\begin{array}{ccc}cos2\alpha &sin2\alpha \\-sin2\alpha &cos2\alpha \\\end{array}\right]$