If [(cosa, -sina)(sina,cosa)] then find the least value of α for which A + A’ = I.

Question

If A = \( \begin{bmatrix} cos a&-sina \\[0.3em] sina & cosa \\[0.3em] \end{bmatrix}\) then find the least value of α for which A + A’ = I.

A = [(cosa, -sina)(sina,cosa)]

Answer 1

We are given that A + A’ = I

On comparing the elements we get,

2cosa = 1

This implies, cosa = \(\frac{1}{2}\)

For a belongs 0 to \(\pi\), a = \(\frac{\pi}{3}\)