Evaluate the following: ` |[cosalpha, sinalpha],[sinalpha, cosalpha]| `

Evaluate the following: |[tanalpha, cosecalpha],[sinalpha, cotalpha]|

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 A=[ [0,-tan((alpha)/2)],[tan(alpha/2),0]] then (I-A)[[cosalpha,-sinalpha],[sinalpha,cosalpha]] =

If A= [[cosalpha,sinalpha],[-sinalpha,cosalpha]] then show that A^2=[[cos2alpha,sin2alpha],[-sin2alpha,cos2alpha]]

If A=[[cosalpha, sinalpha],[-sinalpha, cosalpha]] , prove by mathematicasl induction that, A^n=[[cosnalpha, sin nalpha],[-sin nalpha,cos nalpha]] for every natural number n

Evaluate: =|[0,sinalpha,-cosalpha],[-sinalpha,0,sinbeta],[cosalpha,-sinbeta,0]|

Find the inverse of [(1, 0, 0),( 0,cosalpha,sinalpha),(0,sinalpha,-cosalpha)]

Find the inverse the matrix (if it exists)given in [(1, 0, 0),( 0,cosalpha ,sinalpha),(0, sinalpha, -cosalpha)]

If A(alpha,beta)=[[cosalpha,sinalpha,0],[-sinalpha,cosalpha,0],[ 0, 0,e^(beta)]],t h e nA(alpha,beta)^(-1) is equal to a. A(-alpha,-beta) b. A(-alpha,beta) c. A(alpha,-beta) d. A(alpha,beta)

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