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2 solutions
Good solution
I don't understand what you mean by the following statement:
a × b is only valid for ( a , b ) are positive integers.
Did you mean to say that a × b = a b is valid only for non-negative reals a , b ?
EDIT: This was a bit flawed since the "valid only" term is not necessarily true (can be seen in the counter-example I gave).
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Arghh. Sorry :3
Edited. Thanks.
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Check again. It's not fixed yet. That identity holds for all non-negative reals a , b , not just for positive integers a , b .
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@Prasun Biswas – Fine now?? :3 :3 :3
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@Mehul Arora – Wait, I think I have a problem with the "valid only" part. That identity does hold sometimes when one of a or b is negative. Let me give the counter-example in another comment.
Here's a counter-example to your "only valid for" claim. Consider a = ( − 4 ) and b = 9 . Now, we have,
a b = − 3 6 = 6 i and a × b = 2 i × 3 = 6 i
You can see that the identity holds even though a is negative. I would say that you should edit your solution to reflect that the identity you stated holds for all non-negative reals but fails to hold for some non-negative reals.
− 9 × − 4 = − 1 9 × − 1 4 = − 1 ( 2 2 3 2 ) = − 6
You forgot Cheers xD
Good solution , upvoted
a × b = a b is only valid for ( a , b ) are non negative integers.
Hence, We have to bring complex numbers into play.
→ i 9 × i 4
Here, i is a complex number which satisfies i 2 = − 1
→ i 2 × 3 × 2
→ − 6
Which is our answer.
Cheers!