If `A=(1)/(3)[[2,-2,1],[1,2,2],[2,1,-2]]`, find |AA'|

If A=[[1,2,3],[-1,0,2],[1,-3,1]], B=[[4,5,6],[-1,0,1],[2,1,2]], C=[[-1,-2,1],[-1,2,3],[-1,-2,2]] find A-2B+3C

If A=[[1, 1,-2],[ 2, 1,-3],[ 5, 4,-9]] . Find |A| .

If A=[[-1,-1,3],[1,2,4],[2,-1,3]],B=[[1,-2,5],[0,-2,2],[1,2,-3]],C=[[-2,1,2],[1,1,2],[2,0,1]] then find A+B+C

If A=[[0 ,1 ,3],[ 1, 2,x],[2, 3, 1]] and A^(-1)=[[1//2,-4 ,5//2],[-1//2, 3,-3//2],[ 1//2,y,1//2]] ,find x ,\ y .

If A=[(1,2,3),(2,1,2),(2,2,3)]B=[(1,2,2),(-2,-1,-2),(2,2,3)] and C=[(-1,-2,-2),(2,1,2),(2,2,3)] then find the value of tr. (A+B^(T)+3C) .

If A=[{:(,2,1,-1),(,0,1,-2):}] find: (i) A^(t).A (ii) A.A^(t) where A^t is the transpose of matrix A.

If A=[[1,2,3],[2,0,-2]],B=[[1,1,-1],[2,0,3],[3,-1,2]] and C=[[1,3],[0,2],[-1,4]] find A(BC).

If A = |{:(1,1,-2),(2,1,-3),(5,4,-9):}| , find |A|.

Find x and y i the matrix A= 1/3 [[1,2,2],[2,1,-2],[x,2,y]] satisfythe condition A A\'=A\'A=I_3

If A=[[1,2,-3] , [5,0,2] , [1,-1,1]] and B=[[3,-1,2] , [4,2,5] , [2,0,3]] then find matrix C such that A+2C=B