If `0 < A < B < pi , sinA+sinB=sqrt(3/2)` and `cos A+ cos B=1/sqrt2` then `A=`

If A = [{:( 0,0,0),(0,0,0) ,(0,1,0):}] ,then A is

If A = [{:( 0,0,0),( 1,0,0),(0,1,0):}] ,then

If A =[{:(2,0,0),(0,3,0),(0,0,5):}] , prove that, A^(2)=[{:(2^(2),0,0),(0,3^(2),0),(0,0,5^(2)):}] , hence by induction method show that, A^(n)=[{:(2^(n),0,0),(0,3^(n),0),(0,0,5^(n)):}]

If P = [(x,0,0),(0,y,0),(0,0,z)]and Q = [(a,0,0),(0,b,0),(0,0,c)] , verify that PQ = QP = [(xa, 0,0),(0,yb,0),(0,0,zc)]

If A =[{:(a,0,0),(0,a,0),(0,0,a):}] , then det (adjA) equals