If `A=[(costheta,-sintheta),(sintheta,costheta)],` then find the values of `theta` satisfying the equation `A^T+A=I_2`.

Options

A. `theta =n p, n in Z`
B. `0=(2n+1)pi/2,n in Z`
C. `theta=2n p+pi/3,n in Z`
D. none of these

Answer

C

Explanation

We have,
`A^T+A=I_2`
`rArr {:[(costheta,sintheta),(-sintheta,costheta)]+[(costheta,-sintheta),(sintheta,costheta)]=[(1,0),(0,1)]:}`
`rArr{:[(2costheta,0),(0,costheta)]=[(1,0),(0,1)]:}`
`rArr costheta=1/2=cos.(pi)/3rArrtheta=2npipmpi/3,n inZ`