If `A=[cosalphasinalpha-sinalphacosalpha]` , then verify that `A^T\ A=I_2` .

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] , then verify that A^T\ A=I_2 .

If A=[cos alpha sin alpha-sin alpha cos alpha], then verify that A^(T)A=I_(2)

If (i) A=[cosalphasinalpha-sinalphacosalpha] , then verify that AprimeA" "=" "I . (ii) A=[sinalphacosalpha-cosalphasinalpha] , then verify that AprimeA" "=" "I .

If A=[(cos alpha,sinalpha),(-sinalpha,cosalpha)] , verify that A'A=I_2

If (i) A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] then verify that A'A=I. (ii) A=[{:(sinalpha,cosalpha),(-cosalpha,sinalpha):}] then verify that A'A=I.

If (i) A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] , then verify that AprimeA" "=" "I . (ii) A=[[sinalpha,cosalpha],[-cosalpha,sinalpha]] , then verify that AprimeA" "=" "I .

If (i) A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] , then verify that AprimeA = I .(ii) A=[[sinalpha,cosalpha],[-cosalpha,sinalpha]] , then verify that AprimeA = I .

If A_alpha=[cosalphasinalpha-sinalphacosalpha] , then prove that (A_alpha)^n=[cos n\ alphasinn\ alpha-sinn\ alpha cos n\ alpha] for every positive integer n .

If A=[[sinalpha,cosalpha],[-cosalpha,sinalpha]] , verify that A^T A=I_2

If A,=[[sin alpha,cos alpha-cos alpha,sin alpha]], verify that A^(T)A=I_(2)