Evaluate `Delta=|[0, sin alpha, -cos alpha],[ -sin alpha, 0 , sin beta],[ cos alpha, -sin beta, 0]|`

Evaluate |[cos alpha cos beta, cos alpha sin beta, -sin alpha],[ -sin beta, cos beta, 0],[ sin alpha cos beta, sin alpha sin beta, cos alpha]|

if A=[[sin alpha, cos alpha],[-cos alpha, sin alpha]] , then verify A^T A=I

Find inverse of the matrix A=[[cos alpha, -sin alpha, 0 ],[ sin alpha, cos alpha, 0],[ 0, 0, 1]]

If cos alpha + sin alpha = (3)/(4) , then sin^(6) alpha + cos^(6) alpha is equal to

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 a) A(-alpha, -beta) b) A(-alpha,beta) c) A(alpha, - beta) d) A(alpha, beta)

If A = [(cos alpha,sin alpha),(-sin alpha,cos alpha)] then A^(10) is equal to

Let lambda and alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+ (sin alpha) y + (cos alpha)z = 0 , x + (cos alpha) y + (sin alpha) z = 0 , -x + (sin alpha) y - (cos alpha) z = 0 has a non trivial solution then S contains a) (-1,1) b) [-sqrt2,-1] c) [1,sqrt2] d) [-sqrt2,sqrt2]

If A=[[cos alpha, -sin alpha],[sin alpha, cos alpha]] , then A+A^T=I if the value of alpha is

The distance between the points (a cos alpha, a sin alpha) and (a cos beta, a sin beta) is a) 2|sin((alpha-beta)/(2))| b) 2|a sin((alpha-beta)/(2))| c) 2|a cos((alpha-beta)/(2))| d) |a cos((alpha-beta)/(2))|