यदि `A=[(-1,-1,-1),(3,-3,3),(5,-5,5)], B=[(0,4,3),(1,-3,-3),(-1,4,4)], A^(2).B^(2)` का मान ज्ञात कीजिये।

Explanation

हम जानते हैं की
`A^(2)=A.A`
`=[(-1,1,-1),(3,-3,3),(5,-5,5)].[(-1,1,-1),(3,-3,3),(5,-5,5)]`
`=[(1+3-5,-1-3+5,1+3-5),(-3-9+15,3+9-15,-3-9+15),(-5-15+25,5+15-25,-5-15+25)]`
`=[(-1,1,-1),(3,-3,3),(5,-5,5)]`
इसी प्रकार
`B^(2)=B.B`
`=[(0,4,3),(1,-3,-3),(-1,4,4)].[(0,4,3),(1,-3,-3),(-1,4,4)]`
`=[(0+4-3,0-12+12,0-12+12),(0-3+3,4+9-12,3+9-12),(0+4-4,-4-12+16,-3-12+16)]`
`=[(1,0,0),(0,1,0),(0,0,1)]`
अन्ततः `A^(2).B^(2)=[(-1,1,-1),(3,-3,3),(5,-5,5)][(1,0,0),(0,1,0),(0,0,1)]`
`=[(-1,1,-1),(3,-3,3),(5,-5,5)]`