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If A=[{:(2, 1,),(4,2,)],B =[{:(2,3,4),(1...

If `A=[{:(2, 1,),(4,2,)],B =[{:(2,3,4),(1,4,0):}]` and `C=[{:(-1,2,1),(1,0,2):}]` then veri fy that `A(B+C)=(AB+AC)`.

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We h ave to verify that `A(B+C)=AB+AC`
we have, `A=[2,1],B=[{:(5,3,4),(8,7,6):}]` and `C=[{:(-1,2,1),(1,0,2):}]`
`therefore A(B+C)= [2,1][{:(5-1,3+2,4+1),(8+1 , 7+0,6+2):}]`
`=[2,1][{:(4,5,5),(9,7,8):}]`
`=[8+9 10 +7 10+8]`
`=[17 17 18]`
Also, `AB= [2,1][-1,2,1),(1,0,2):}]`
`=[-2+1 4+0 202]=[ -1 4 4]`
`therefore AB+AC =[18 13 14 ] +[-1 4 4] `
`=[17 17 18]`
`therefore A(B+C)=(AB+AC)`
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