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Question
Let A =`[[-1 1 -1],[3 -3 3],[5 5 5]]`and B =`[[0 4 3],[1 -3 -3],[-1 4 4]]`
, compute A2 − B2.
Solution
Given : A= `[[-1 1 -1],[3 -3 3],[5 5 5]]`
Now,
`A^(2)=A A`
`⇒A^(2)=[[-1 1 -1],[3 -3 3],[5 5 5]]` `[[-1 1 -1],[3 -3 3],[5 5 5]]`
`⇒A^(2)=[[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]]`
`⇒A^(2)=[[-1 -9 -1],[3 27 3],[35 15 35]]`
`B^(2)=B B`
`⇒B^(2)=[[0 4 3],[1 -3 -3],[-1 4 4]]` `[[0 4 3],[1 -3 -3],[-1 4 4]]`
`⇒B^(2)=[[0+4-3 0-12+12 0-12+12],[0-3+3 4+9-12 3+9-12],[0+4-4 -4-12+12 -3-12+16]]`
`⇒B^(2)= [[1 0 0],[0 1 0],[0 0 1]]`
`A^2−B^2 `
`⇒A^2−B^2= [[-1 -9 -1],[3 27 3],[35 15 35]]-[[1 0 0],[0 1 0],[0 0 1]]`
`⇒A^2−B^2= [[-1-1 -9-0 -1-0],[3-0 27-1 3-0],[35-0 15-0 35-1]]`
`⇒A^2−B^2= [[-2 -9 -1],[3 26 3],[35 15 34]]`
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