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]]`

Explanation

(i) Taking L.H.S
`[[5,-1],[ 6 ,7]][[2, 1],[ 3 ,4]]`
`=[[5xx2+(-1)xx3,5xx1+(-1)xx4],[6xx2+7xx3,6xx1+7xx4]]`

`=[[10-3,5-4],[12+21,6+28]]`

`=[[7,1],[33,34]]`
Taking R.H.S
`[[2, 1],[ 3, 4]][[5,-1],[ 6, 7]]` ,

`=[[2xx5+1xx6,2xx(-1)+1xx7],[3xx5+4xx6,3xx(-1)+4xx7]]`

`=[[10+6,-2+7],[15+24,-3+28]]`

`=[[16,5],[39,35]]`
`ne`L.H.S

Thus, L.H.S`ne` R.H.S
Hence Proved.

(ii) Taking L.H.S.
`[[1, 2, 3],[ 0, 1, 0],[ 1, 1, 0]][[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]]`

`=[[1xx(-1)+2xx0+3xx2,1xx1+2xx(-1)+3xx3,1xx0+2xx1+3xx4],[0xx(-1)+1xx0+0xx2,0xx1+1xx(-1)+0xx3,0xx0+1xx1+0xx4],[1xx(-1)+1xx0+0xx2,1xx1+1xx(-1)+0xx3,1xx0+1xx1+0xx4]]`

`=[[-1+0+6,1-2+9,0+2+12],[0+0+0,0-1+0,0+1+0],[-1+0+0,1-1+0,0+1+0]]`

`=[[5,8,14],[0,-1,1],[-1,-1,1]]`
Taking R.H.S.
`[[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]][[1 ,2 ,3],[ 0, 1, 0],[ 1, 1, 0]]`

`[[-1xx1+1xx0+0xx1,-1xx2+1xx1+0xx1,-1xx3+1xx0+0xx0],[0xx1+(-1)xx0+1xx1,0xx2+(-1)xx1+1xx1,0xx3+(-1)xx0+1xx0],[2xx1+3xx0+4xx1,2xx2+3xx1+4xx1,2xx3+3xx0+4xx0]]`

`=[[-1+0+0,-2+1+0,-3+0+0],[0+0+1,0-1+1,0+0+0],[2+0+4,4+3+4,6+0+0]]`

`=[[-1,-1,-3],[1,0,0],[6,11,6]]`

`ne` L.H.S

Thus, L.H.S`ne` R.H.S
Hence Proved.