How to solve this determinant without expanding it
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If two rows or columns of the determinant are same then the value of the determinant is 0. Take 5^2 common from 1st row and then take 5^3 common from 2nd row. then you will get the first as well as the second rows equal to 1 5 5^2. Since both rows are same the value of the determinant will be 0 (zero).
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