If `A=(cosalpha-sinalpha0sinalphacosalpha0 0 0 1),` find `a d jdotA` and verify that `A(a d jdotA)=(a d jdotA)A=|A|I_3dot`

If A=[(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),( 0, 0, 1)], find a d jdotA and verify that A(a d jdotA)=(a d jdotA)A=|A|I_3dot

If A=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]] , find a d j\ A and verify that A(a d j\ A)=(a d j\ A)A=|A|I_3 .

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :

Find the adjoint of the following matrices: [(cosalpha,sinalpha),(sinalpha,cosalpha)] (ii) [(1,tanalpha//2),(-tanalpha//2, 1)] Verify that (a d j\ A)A=|A|I=A(a d j\ A) for the above matrices.

If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n prove that [F(alpha)]^(-1)=F(-alpha)dot

If A=[{:(sinalpha,-cosalpha,0),(cosalpha,sinalpha,0),(0,0,1):}] then A^(-1) is equal to

Let F(alpha)=[cosalpha-sinalpha0sinalphacosalpha0 0 0 1] and G(beta)=[cosbeta0sinbeta0 1 0-sinbeta0cosbeta] . Show that [F(alpha)]^(-1)=F(-alpha) (ii) [G(beta)]^(-1)=G(-beta) (iii) [F(alpha)G(beta)]^(-1)=G(-beta)F(-alpha) .

If A=[[cosalpha,-sinalpha],[sinalpha,cosalpha]] , then A+A^(prime)=I , if the value of alpha is (A) pi/6 (b) pi/3 (c) pi (d) (3pi)/2

Evaluate Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

Let A(alpha)=[cosalpha0sinalpha0 1 0sinalpha0cosalpha] and X is a set of all matrices A(alpha) for different values of alpha . Which of the following is true (a)A^(-1)(alpha)=A(-alpha) (b) A^(-1)(alpha)=A(alpha) (c)det(a d j(A^(-1)(alpha)))=sec^2 2alpha (d)det(A^(-1)(alpha))=1/(cos2alpha)