If the lines `lambdax + (sinalpha)y + cosalpha =0, x+cosalpha y+sinalpha=0,x-sinalpha y+cosalpha=0` pass through the point where `alpha in R` the `lambda` lies in the interval

If A=[(cas alpha, sinalpha),(-sinalpha,cosalpha)], AA'=

The distance the points (sinalpha, cosalpha,0), (cosalpha, - sin alpha,0) is

If A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] , then

Assertion : The system of linear equations x+(sinalpha)y+(cosalpha)z=0x+(cosalpha)y+(sinalpha)z=0x-(sinalpha)y-(cos\ alpha)z=0 has a non-trivial solution for only value of alpha lying the interval (0,\ pi) Reason: The equation in\ alpha cosalphas in alpha cosalphasinalpha cosalphasinalphac osalpha-sinalpha-cosalpha|=0 has only one solution lying in the interval (-pi/4,\ pi/4)

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] is such that A^T=A^(-1) , find alpha .

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] is such that A^T=A^(-1) , find alpha

If F(alpha)=[[cosalpha, -sinalpha, 0], [sinalpha, cosalpha, 0], [0, 0, 1]] , where alphainR , then (F(alpha))^(-1)=

If A_(alpha)=[(cosalpha,sinalpha),(-sinalpha,cosalpha)] then (A_(alpha))^2=?