If (i) `A=[cosalphasinalpha-sinalphacosalpha]` , then verify that `AprimeA" "=" "I` . (ii) `A=[sinalphacosalpha-cosalphasinalpha]` , 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=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] , then verify that A^T\ A=I_2 .

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

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

If z=4 + 3i , then verify that |z|= |bar(z)|

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 .

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 z=4 + 3i , then verify that -|z| lt I m (z) le |z|