Find the inverse of each of the matrices.
`[[1, 0, 0],[ 0 , cos alpha, sin alpha],[ 0, sin alpha, -cos alpha]]`

Find the inverse of each of the matrices [[1, 2, 3],[ 0, 2, 4],[ 0, 0, 5]]

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

If A=[[0, -tan (alpha/2)], [ tan (alpha/2), 0]] and I is the identity matrix of order 2 , show that I+A=(I-A)[[cos alpha, -sin alpha],[ sin alpha, cos alpha]]

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^(10) is equal to

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

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

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_(alpha)=[[cos alpha, sin alpha],[ -sin alpha , cos alpha]] , then prove that i) A_(alpha ). A_(beta)=A_(alpha + beta) ii) (A_alpha)^n=[[cos n alpha, sin n alpha],[ -sin n alpha, cos n alpha]] for every positive integer n .

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