If `A=[[1,1,1],[1,2,-3],[2,-1,3]]` Find `A^2`.

If A = [[2,0,1],[2,-1,3],[1,1,0]] then find A^2-3A+2I .

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=[[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=[[0, 1,2],[1,2,3],[3,a,1]]and A^(-1)[[1//2,-1//2,1//2],[-4,3,b],[5//2,-3//2,1//2]] then find a and b

Consider the matrix A=[[2,1,3],[2,3,1],[1,1,1]] B=[[-1,2,3],[-2,3,1],[-1,1,1]] Find A+B

Consider the matrix A=[[2,1,3],[2,3,1],[1,1,1]] B=[[-1,2,3],[-2,3,1],[-1,1,1]] Find (A+B)(A-B)

If A=[[2,3,2] , [1,2,2] , [-3,1,-1]] then find A^-1 using elementary transformations

Find the rank of A=[[1,1,-1,1],[1,3,2,1],[2,0,3,2],[3,3,3,3]]

If P=[[1,2,-3] , [3,-1,2] , [-2,1,3]], Q=[[2,3,1] ,[3,1,2] , [1,2,3]] then find the matrix R such that P+Q+R is a zero matrix

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).