Show that
i) `[[5 , (-1)],[ 6, 7]][[2, 1],[ 3 ,4]] ne[[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]] ne[[(-1), 1, 0],[ 0, (-1), 1],[ 2, 3, 4]] [[1 , 2, 3],[ 0, 1, 0],[ 1, 1, 0]]` .

Show that [[5,-1],[6,7]] [[2,1],[3,4]] ne [[2,1],[3,4]] [[5,-1],[6,7]]

Show that [[1,2,3],[0,1,0],[1,1,0]] [[-1,1,0],[0,-1,1],[2,3,4]] ne [[-1,1,0],[0,-1,1],[2,3,4]][[1,2,3],[0,1,0],[1,1,0]]

Compute the indicated products. i) [[a , b],[ -b , a]] [[a, -b],[ b, a]] ii) [[1], [ 2], [3]][[2, 3 ,4]] iii) [[1, (-2)],[ 2 ,3]] [[1 , 2 ,3],[ 2, 3 , 1]] iv) [[2 , 3 , 4 ],[ 3 , 4 , 5 ],[ 4, 5 ,6]] [[1 , -3, 5],[ 0, 2, 4],[ 3, 0, 5]] v) [[2 , 1],[ 3 , 2],[ (-1), 1]] [[1, 0 , 1],[ (-1), 2, 1]] vi) [[3, (-1), 3],[ (-1), 0, 2]][[2, -3],[ 1 , 0],[ 3, 1]]

Find A^2-5 A+6 I , if A=[[2, 0, 1],[ 2 ,1 , 3],[ 1, -1, 0]]

Find x , if [[x,-5,-1]] [[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]][[x],[ 4],[ 1]]=0

Evaluate the determinants (i) |[3 , -1, -2],[ 0, 0, -1],[ 3, -5, 0]| (ii) |[3 , -4, 5],[ 1, 1, -2],[ 2, 3, 1]| iii) |[0, 1, 2],[ -1, 0, -3],[ -2, 3, 0]| iv) |[2, -1, -2],[ 0, 2, -1],[ 3, -5, 0]|

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

If A=[[-1, 2, 3],[ 5, 7, 9],[ -2, 1 , 1]] and B=[[-4 , 1, -5],[ 1, 2, 0],[ 1, 3, 1]] then verify that (i) (A+B)^'=A^'+B^'

If A=[[1 , 2 , 3],[ 3, -2 , 1],[ 4, 2 , 1]] , then show that A^3-23 A-40 I=0

Complete the following product [[1 , 0 , -5],[ 2, 0, 4]][[3 , 1],[ 0 , -1],[ 0, 5]]