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Question

If A=[1001] and B=[0110], find AB and BA. Prove that ABBA.

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Solution

Given: A=[1001] and B=[0110]
Now,
AB=[1001][0110]
AB=[1(0)+0(1)1(1)+0(0)0(0)+(1)(1)0(1)+(1)(0)]
AB=[0+01+0010+0]
AB=[0110] (1)

BA=[0110][1001]
BA=[0(1)+1(0)0(0)+1(1)1(1)+0(0)1(0)+0(1)]
BA=[0+0011+00+0]
BA=[0110] (2)
From equation (1) and (2)
BAAB.
Hence proved.

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