(i) यदि `A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}]` कीजिए कि A ' A = I.
(ii) यदि `A=[{:(sinalpha,cosalpha),(-cosalpha,sinalpha):}]` हो तो सत्यापित कीजिए कि A'A=I.

Explanation

(i) `A=[{:(sinalpha,cosalpha),(-sinalpha,cosalpha):}]`
`rArrA'=[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}]`
`thereforeA'A=[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}][{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}]`
`=[{:(cos^(2)alpha+sin^(2)alpha,sinalphacosalpha-sinalphacosalpha),(sinalphacosalpha-sinalphacosalpha," "sin^(2)alpha+cos^(2)alpha):}]`
`=[{:(1,0),(0,1):}]=I` यही सत्यापित करना था ।
(ii) `A'=[{:(sinalpha,cosalpha),(-cosalpha,sinalpha):}]`
`rArrA'=[{:(sinalpha,-cosalpha),(cosalpha,sinalpha):}]`
`thereforeA'A=[{:(sinalpha,-cosalpha),(cosalpha,sinalpha):}][{:(sinalpha,cosalpha),(-cosalpha,sinalpha):}]`
`=[{:(sin^(2)alpha+cos^(2)alpha,sinalphacosalpha-sinalphacosalpha),(sinalphacosalpha-sinalphacosalpha," "cos^(2)alpha+sin^(2)alpha):}]`
`=[{:(1,0),(0,1):}]=I` यही सत्यापित करना था ।