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प्रश्न
If possible, find BA and AB, where A = `[(2, 1, 2),(1, 2, 4)]`, B = `[(4, 1),(2, 3),(1, 2)]`
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उत्तर
BA = `[(4, 1),(2, 3),(1, 2)]_(3 xx 2) [(2, 1, 2),(1, 2, 4)]_(2 xx 3)`
BA = `[(8 + 1, 4 + 2, 8 + 4),(4 + 3, 2 + 6, 4 + 12),(2 + 2, 1 + 4, 2 + 8)]_(3 xx 3)`
= `[(9, 6, 12),(7, 8, 16),(4, 5, 10)]_(3 xx 3)`
Now AB = `[(2, 1, 2),(1, 2, 4)]_(2 xx 3) [(4, 1),(2, 3),(1, 2)]_(3 xx 2)`
= `[(8 + 2 + 2, 2 + 3 + 4),(4 + 4 + 4, 1 + 6 + 8)]_(2 xx 2)`
= `[(12, 9),(12, 15)]_(2 xx 2)`
Hence, BA = `[(9, 6, 12),(7, 8, 16),(4, 5, 10)]` and AB = `[(12, 9),(12, 15)]`.
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