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Let A=[(-1, 1,-1 ),(3,-3, 3 ),(5, 5, 5)]...

Let `A=[(-1, 1,-1 ),(3,-3, 3 ),(5, 5, 5)]` and `B=[(0 ,4 ,3),( 1,-3,-3),(-1, 4 ,4)]` , compute `A^2-B^2` .

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Given,
`A=[(-1, 1,-1 ),(3,-3, 3 ),(5, 5, 5)]`
`B=[(0 ,4 ,3),( 1,-3,-3),(-1, 4 ,4)]`
`A^2=[(-1, 1,-1 ),(3,-3, 3 ),(5, 5, 5)]xx[(-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,-9,-1),(3,27,3),(35,15,35)]`
`B^2=[(0 ,4 ,3),( 1,-3,-3),(-1, 4 ,4)]xx[(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+12-12)]`
`=[(1,0,0),(0,1,0),(0,0,-3)]`
`A^2-B^2`
`=[(-1,-9,-1),(3,27,3),(35,15,35)]-[(1,0,0),(0,1,0),(0,0,-3)]`
`=[(-2,-9,-1),(3,26,3),(35,15,38)]`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
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