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If `A=[[sinalpha,cosalpha],[-cosalpha,sinalpha]]`, verify that `A^T A=I_2`

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`A=[[sinalpha,cosalpha],[-cosalpha,sinalpha]]`
`A^T * A = I_2`
LHS `= [[Sin alpha,-cos alpha],[cos alpha,sin alpha]]` `[[Sin alpha,cos alpha],[-cos alpha,sin alpha]]`
`=[[sin^2 alpha + coz^2 alpha, sin alpha cos alpha – cos alpha sin alpha],[cos alpha sin alpha – sin alpha cos alpha, cos^2 alpha + sin^2 alpha]]`
`=[[1,0],[0,1]]`
`=I_2`
`=RHS` Hence LHS = RHS
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