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

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

If A=[(cos alpha, -sin alpha),(sin alpha, cos alpha)], and A+A'=I , then the value of alpha is

If A=[[cos alpha, -sin alpha],[ sin alpha, cos alpha]] , then the number of values of alpha in (0, pi) satisfying A+A^T=I_, is [Note: I is an identity matrix of order 2 and P^T denotes transpose of matrix P .]

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=[(0,-tan alpha),(2,tan alpha),(2,0)] and I is 2 xx 2 unit matrix, then (I-A)[(cos alpha,sin alpha),(sin alpha, sin alpha)] is (a) -I+A (b) I-A (c) -I-A (d) non of these

If F(alpha)=[[cos alpha,0,sin alpha],[0,1,0],[-sin alpha,0,cos alpha]] , show that [F(alpha]^(-1)=F(-alpha) .

IF tan alpha = ( sin alpha - cos alpha )/( sin alpha + cos alpha) , then sin alpha + cos alpha is

sin 3 alpha = 4 sin alpha sin(x + alpha) sin(x-alpha)