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Question
If P = `|(1 , 2),(2 , 1)|` and Q = `|(2 , 1),(1 , 2)|` find P (QP).
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Solution
P = `|(1 , 2),(2 , 1)|_(2 xx 2)` , Q = `|(2 , 1),(1 , 2)|_(2 xx 2)`
QP = `|(2 , 1),(1 , 2)| |(1 , 2),(2 , 1)|`
`= |(2 + 2, 4 + 1),(1 + 4, 2 + 2)|`
`= |(4 , 5),(5 , 4)|_(2 xx 2)`
P(QP) = `|(1 , 2),(2 , 1)| |(4 , 5),(5 , 4)|`
`= |(4 + 10 , 5 + 8),(8 + 5 , 10 + 4)|`
`= |(14 , 13),(13 , 14)|_(2 xx 2)`
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