IF`A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}]`, then show that AA'=A'A

If A = [(cos alpha, sin alpha),(-sin alpha, cos alpha)] , then show that AA'= A'A.

If A=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] , then verify that A'A=I

If A=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] then "AA"^(T)=

Find the adjoint and inverse of the matrix [{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}]

If A=[(cos alpha, -sinalpha),(sin alpha, cos alpha)] , then A+A^(T)=I , if the vlaue of alpha is

If A=[(sin alpha, cos alpha),(-cos alpha, sin alpha)] , then verify that A'A=I

If A=[(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1)] then ("Adj A")^(-1) =

Assertion (A) : The matrix [(cosalpha,sinalpha),(-sinalpha,cosalpha)] is an orthogonal matrix. Reason (R) : If A is an orthogonal matrix then A A^(T)=A^(T)A=I

Statement-I : Let A(0,0),B(cosalpha,sinalpha),C(sinalpha-cosalpha) are vertices of a trianlge then the locus of the centroid of triangle is 9x^(2)+9y^(2)=4 Statement-II : The locus of the point (acostheta,bsintheta) is (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 The correct statement is