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View the matrix I know how to do the inverse and think I know the right answer in modulo 5 but need to make sure thanks

Dino Walters
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  • Welcome to Math.SE! If you think you know the answer, it would be helpful if you write it down. – Hrodelbert Aug 26 '15 at 09:53
  • I would be very curious to see how to do inverses modulo $5$, could you, please, include your solution to the question? – A.Γ. Aug 26 '15 at 09:58
  • Could you show us how you would do the inverse over $\Bbb{F}_5$? If there is an error then perhaps someone here can point it out to you. Also, if you think you have the right answer, you can just check it by multiplying the two matrices. – Servaes Aug 26 '15 at 10:06
  • What I thought is we could do the inverse on its own and then adapt it to modulo 5.But the answer comes out in fractions and im not sure if thats correct – Dino Walters Aug 26 '15 at 10:07
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    The same algorithm works over any field. Here's one example modulo 29. Your numbers will be simpler. I didn't check, so it is possible that you will try and divide by five, which in this case is a no-no, because it amounts to attempting to divide by zero. – Jyrki Lahtonen Aug 26 '15 at 10:23
  • You do it in the usual way: simultaneous row operations on the matrix and on the identity matrix, but the computations are made modulo $5$. – Bernard Aug 26 '15 at 10:28

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I am afraid that your matrix isn't invertible when entries are in $\mathbb{F_5}$, because its determinant is $-5$ in $\mathbb{Q}$, which is $0$ in $\mathbb{F_5}$.

Alternatively, note that 2 times the first row plus 2 times the second row is the third row, with operation in $\mathbb{F_5}$.

pisco
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