If `A=[[6,2,7],[-1,3,1],[1,-3,0]]`, then `|A|=?`

If A=[[7,-3,-3],[-1,1,0],[-1,0,1]] then A^(-1) is

If A^(-1)=[[1,-1, 2],[0, 3,1],[ 0 ,0,-1/3]] , then |A|=-1 b. adj A=[[-1, 1 ,2],[ 0,-3,-1],[ 0, 0, 1/3]] c. A=[[1, 1/3, 7 ],[0, 1/3, 1],[0 ,0,-3]] d. A =[[1,-1/3,-7],[ 0,-3, 0],[ 0, 0, 1]]

If A=[[1,2,1] , [1,-4,1] , [3,0,-3]], B=[[2,1,1] , [1,-1,0] , [2,1,-1]] then show that AB=6I_3

If A=[[1,4],[0,5],[6,7]] and B=[[2,3,-1],[1,0,-7]] , verify that (AB)\'=B\'A\'

If A=[[1,0,5],[3,2,7],[5,4,8]],B=[[3,1,2],[9,0,-6],[7,4,1]],C=[[2,0,-1],[7,5,6],[1,1,4]] , verify that A+(B+C)=(A+B)+C

(D) Find the rank of the matrix A= [[1,2,3,0],[2,4,3,2],[3,2,1,3],[6,8,7,5]]

Show that(i) [[5,-1],[ 6 ,7]][[2, 1],[ 3 ,4]]!=[[2, 1],[ 3, 4]][[5,-1],[ 6, 7]] (ii) [[1, 2, 3],[ 0, 1, 0],[ 1, 1, 0]][[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]]!=[[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]][[1 ,2 ,3],[ 0, 1, 0],[ 1, 1, 0]]

If A={:[(3,2,7),(1,1,4),(-1,-1,0)]:},B={:[(1,0,3),(2,1,0),(0,-1,-3)]:}andC{:[(1,0,0),(0,1,0),(0,0,1)]:} , then find 2A+3B-7C.

If A=[[1,0,20,2,12,0,3]], prove that A^(3)-6A^(2)+7A+2I=0