If `A=[[-1, 0 ,0], [0,-1, 0], [0, 0,-1]]` , find `A^2` .

If A=[[-1, 0, 0], [0,-1, 0], [0, 0,-1]] , find A^3 .

If A=[[1,0,0],[0,1,0],[a,b,-1]] , find A^2

If A=[[1, 0],[ 0,-1]] and B=[[0 ,1], [1, 0]] , then find AB,BA. Show that 'A B!=B A .

If A=((-1, 2, 0), (-1, 1, 1), (0, 1, 0)) , find A^(-1) . Use it to solve the system of equations: -x+2y=2, -x+y +z=1, y+2=0 .

If A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] find AB and BA.

If A= [[1 , 0],[ − 1, 7]] and I=[[1, 0],[ 0 ,1]] , then find k so that A^2=8A+k I

If x ,\ y ,\ z are non-zero real numbers, then the inverse of the matrix A=[[x,0, 0],[ 0,y,0],[ 0, 0,z]] , is (a) [[x^(-1),0 ,0 ],[0,y^(-1),0],[ 0, 0,z^(-1)]] (b) x y z[[x^(-1),0 ,0],[ 0,y^(-1),0],[ 0, 0,z^(-1)]] (c) 1/(x y z)[[x,0, 0],[ 0,y,0],[ 0, 0,z]] (d) 1/(x y z)[[1, 0, 0],[ 0 ,1, 0],[ 0, 0, 1]]

If A=[[1, 0],[ 0, 1]] , B=[[1,0],[0,-1]] and C=[[0, 1],[ 1, 0]] , then show that A^2=B^2=C^2=I_2 .

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 x, y, z are non-zero real numbers, then the inverse of matrix A=[(x,0, 0) ,(0,y,0),( 0, 0,z)] is (A) [[x^(-1),0,0],[0,y^(-1),0],[0,0,z^(-1)]] (B) xyz[[x^(-1),0,0],[0,y^(-1),0],[0,0,z^(-1)]] (C) (1)/(xyz)[[x,0,0],[0,y,0],[0,0,z]] (D) (1)/(xyz)[[1,0,0],[0,1,0],[0,0,1]]