Home
Class 12
MATHS
If A=((alpha,beta),(gamma,-alpha)). such...

If `A=((alpha,beta),(gamma,-alpha))`. such that `A^2=I`. prove that `1-alpha^2-beta gamma=0`

Text Solution

Verified by Experts

Here, `A = [[alpha, beta],[gamma, -alpha]]`
We are given, `A^2 = I`
`:. [[alpha, beta],[gamma, -alpha]] [[alpha, beta],[gamma, -alpha]] = [[1,0],[0,1]]`
`=>[[alpha^2+betagamma, alphabeta -alphabeta],[gammaalpha-gammaalpha, betagamma+alpha^2]] = [[1,0],[0,1]]`
`=> alpha^2+betagamma = 1`
`=>1-alpha^2-betagamma = 0`
Promotional Banner

Similar Questions

Explore conceptually related problems

If A=[[alpha ,beta],[ gamma , -alpha]] is such that A^2=I , then A) 1+alpha^2+beta gamma=0 B) 1-alpha^2+beta gamma=0 C) 1-alpha^2-beta gamma=0^ D) 1+alpha^2-beta gamma=0

If A=[[alpha,betagamma,alpha]] is such that A^(2)=I, then (A)1+alpha^(2)+beta gamma=0(B)1-alpha^(2)+beta gamma,=0(C)1-alpha^(2)-beta gamma,=0(D)1+alpha^(2)-beta gamma=0

If A=[alpha beta gamma-alpha] is such that A^(2)=I, then 1+alpha^(2)+beta gamma=0( b) 1-alpha^(2)+beta gamma=0 (c) 1-alpha^(2)-beta gamma=0 (d) 1+alpha^(2)-beta gamma=0

If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then prove that tan alpha=tan beta+2 tan gamma .

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If alpha,beta,gamma,in(0,(pi)/(2)), then prove that (si(alpha+beta+gamma))/(sin alpha+sin beta+sin gamma)<1

If alpha,beta,gamma, in (0,pi/2) , then prove that (sin(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1