If `A=[[cos alpha,sin alpha],[-sin alpha,cos alpha]]` ,then verify that `A'A=1 `

If A=[[cos alpha,-sin alpha],[sin alpha,cos alpha]], then for what value of alpha is A an identity matrix?

If A=[[cosalpha, -sin alpha] , [sin alpha, cos alpha]] then A+A'=I then alpha=

If A= [[cosalpha,sinalpha],[-sinalpha,cosalpha]] then show that A^2=[[cos2alpha,sin2alpha],[-sin2alpha,cos2alpha]]

If A=[{:(cos alpha,sin alpha),(-sin alpha, cos alpha):}] and A^(-1)=A ' then find the value of alpha .

If A(cos alpha, sin alpha), B(sin alpha, -cos alpha), C(1,2) are the vertices of a triangle, then as alpha varies the locus of centroid of the DeltaABC is a circle whose radius is :

If tan theta=(sin alpha- cos alpha)/(sin alpha+cos alpha) , then:

A=[(cos alpha,-sin alpha),(sin alpha,cos alpha)] and A+A^(T)=I , find the value of alpha .

If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))] , then A(alpha, beta)^(-1) is equal to

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is

One side of a square makes an angle alpha with x axis and one vertex of the square is at origin. Prove that the equations of its diagonals are x(sin alpha+ cos alpha) =y (cosalpha-sinalpha) or x(cos alpha-sin alpha) + y (sin alpha + cos alpha) = a , where a is the length of the side of the square.