If (i) , then verify that (ii) , then verify that
(i)
The given matrix is,
A = [ cos α sin α − sin α cos α ]
The transpose of A is,
A ′ = [ cos α − sin α sin α cos α ]
Calculate A ′ A .
A ′ A= [ cos α − sin α sin α cos α ] [ cos α sin α − sin α cos α ] = [ cos 2 α + sin 2 α sin α cos α − sin α cos α sin α cos α − sin α cos α sin 2 α + cos 2 α ] = [ 1 0 0 1 ] = I
Therefore, it is verified that A ′ A= I .
(ii)
The given matrix is,
A = [ sin α cos α − cos α sin α ]
The transpose of A is,
A ′ = [ sin α − cos α cos α sin α ]
Calculate A ′ A .
A ′ A= [ sin α − cos α cos α sin α ] [ sin α cos α − cos α sin α ] = [ sin 2 α + cos 2 α sin α cos α − sin α cos α sin α cos α − sin α cos α sin 2 α + cos 2 α ] = [ 1 0 0 1 ] = I
Therefore, it is verified that A ′ A= I .
(i)
The given matrix is,
The transpose of A is,
Calculate
Therefore, it is verified that
(ii)
The given matrix is,
The transpose of A is,
Calculate
Therefore, it is verified that
,
then verify that
,
then verify that