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If A=[cosalphasinalpha-sinalphacosalpha]...

If `A=[cosalphasinalpha-sinalphacosalpha]` is such that `A^T=A^(-1)` , find `alpha` .

Text Solution

Verified by Experts

`A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]]`
`|A|=(cosalphaxxcosalpha+sinalphaxxsinalpha)`
`|A|=cos^2alpha+sin^2alpha`
`|A|=1`
Again,
`(adjA)=(A)_T=[[cosalpha,sinalpha],[-sinalpha,cosalpha]]^T`
`=[[cosalpha,-sinalpha],[sinalpha,cosalpha]]`
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