If `A=[[cos alpha,-sin alpha],[sin alpha,cos alpha]],` then for what value of `alpha` is `A` an identity matrix?

Explanation

`A = [[cos alpha,-sin alpha],[sin alpha,cosalpha]]`

For `A` to be an identity matrix,

`A` should be `[[1,0],[0,1]]`.

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

`=>cos alpha = 1 and sin alpha = 0`

`=>cos alpha = cos 0^@ and sin alpha =sin0^@`

`:. alpha = 0`

General solution can be `alpha = 2npi`, where `n` is an integer.