@Aditya Parson
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got it....i really misunderstood the problem ....i thought that there would be only once the number " a" and "b" would be used and as the questioner said that the value would be always zero i thought that the rest terms would be zero....but you showed me my mistake.....thanx for sending...

You wanted to know how many determinants can be formed....see any two determinant can be said different whether its orientation of its terms are different....you are using only 2 non zero element ,you assumed "a" and "b"...now watch that in any place out of the 9 places of a 3 by 3 determinant you put them them and as a result you would get the result zero for every representation......so there are 9 places (3 rows 3 columns ) you are choosing 2 different places out of them .....you could do this in 9C2 ways....so there should (i'm not using "would" as i am not sure for my own logic and apprehension ) be only 36 ways to form different determinant....let's see if any one backs me up for this procedure to be right or wrong......

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how, u came to it...?

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Big solution, too lousy to write it here. Is there any other way to send you my solution.?

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You wanted to know how many determinants can be formed....see any two determinant can be said different whether its orientation of its terms are different....you are using only 2 non zero element ,you assumed "a" and "b"...now watch that in any place out of the 9 places of a 3 by 3 determinant you put them them and as a result you would get the result zero for every representation......so there are 9 places (3 rows 3 columns ) you are choosing 2 different places out of them .....you could do this in 9C2 ways....so there should (i'm not using "would" as i am not sure for my own logic and apprehension ) be only 36 ways to form different determinant....let's see if any one backs me up for this procedure to be right or wrong......

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this is a question which is asked on brilliant

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