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प्रश्न
If A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`, then AB and BA are defined and equal.
पर्याय
True
False
उत्तर
This statement is False.
Explanation:
A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`
Since AB is defined
∴ AB = `[(2, 3, -1),(1, 4, 2)] [(2, 3),(4, 5),(2, 1)]`
= `[(4 + 12 - 2, 6 + 15 - 1),(2 + 16 + 4, 3 + 20 + 2)]`
= `[(14, 20),(22, 25)]`
BA is also defined.
∴ BA = `[(2, 3),(4, 5),(2, 1)] [(2, 3, -1),(1, 4, 2)]`
= `[(4 + 3, 6 + 12, -2 + 6),(8 + 5, 12 + 20, -4 + 10),(4 + 1, 6 + 4, -2 + 2)]`
= `[(7, 18, 4),(13, 32, 6),(5, 10, 0)]`
So AB ≠ BA.
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