If `A=[[cosalpha,-sinalpha],[sinalpha,cosalpha]]`, then `A+A^(prime)=I`, if the value of `alpha`is (A) `pi/6` (b) `pi/3` (c) `pi` (d) `(3pi)/2`

Explanation

`A = [[cos alpha, -sinalpha],[sinalpha, cos alpha]]`

`:. A^T = [[cosalpha, sin alpha],[-sin alpha, cos alpha]]`


We are given, `A + A^T = I`

`:. [[cos alpha, -sinalpha],[sinalpha, cos alpha]]+[[cosalpha, sin alpha],[-sin alpha, cos alpha]] = [[1,0],[0,1]]`

`=>[[2cosalpha,0],[0,2cosalpha]] = [[1,0],[0,1]]`

`:. 2cos alpha = 1`

`=> cos alpha = 1/2`

`=>alpha = pi/3`