" (ii) "|[cos alpha,sin alpha],[sin alpha,cos alpha]|

Write the value of |[[cos alpha,-sin alpha],[sin alpha,cos alpha]] from the following :

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]]

If A= [[cos alpha, -sin alpha],[sin alpha, cos alpha]] , then A + A'= I, the value of a is :

If A(alpha)=[[cos alpha,sin alpha],[-sin alpha,cos alpha]] then A(alpha)A(beta)

If A = [[cos alpha,sin alpha],[-sin alpha,cos alpha]] then prove that, AA'=I. Hence find A^(-1) .

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

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]]

A_(alpha )= [(cos alpha, sin alpha),(- sin alpha, cos alpha)] then prove that (A_(alpha)^(n) = A(n alpha) " where " n in N

A_(alpha )= [(cos alpha, sin alpha),(- sin alpha, cos alpha)] then prove that A_(alpha . A_(beta) = A_(alpha + beta)

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