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प्रश्न
Let A = {a + `sqrt(5)`b : a, b ∈ Z}. Check whether the usual multiplication is a binary operation on A
उत्तर
Let A = `"a" + sqrt(5) "b"` and B = `"C" + sqrt(5)"d"`
Where a, b, c, d ∈ M.
Now A * B = `("a" + sqrt(5)"b")("c" + sqrt(5)"b")`
= `"ac" + sqrt(5)"ad" + sqrt(5)"bc" + sqrt(5)"b" sqrt(5)"d"`
= (ac + 5bd) + `sqrt(5)`(ad+ bc) ∈ A
Where a, b, c, d ∈ Z
So * is a binary operation.
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