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siriusmart

[Unsolved] Magic squares and their Inverse (en.wikipedia.org)

submitted 6 days ago* (last edited 6 days ago) by [email protected] to c/dailymaths

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cross-posted from: https://sopuli.xyz/post/22688165

Random thought on magic squares:

If I view the smallest possible non-trivial magic square
2 7 6
9 5 1
4 3 8
since its rows and diagnoals sum up to 2+5+8 = 2+7+6 = 4+5+6 = 2+9+4 = … = 15

Lets view it as a 3x3 Matrix, its determinant is Δ = -360 . Its inverse:
-37/360 19/180 23/360
17/90 1/45 -13/90
-7/360 -11/180 53/360
note how this is a magic square, rows and diagonals sum up to 1/15.

https://matrix.reshish.com/inverse.php

Now if you are really bored (I can not do this): proof that for any non trivial magic squares the inverse …

exists (i.e. every non-trivial magic square has an inverse)

is a magic square.

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[–] siriusmart 2 points 3 days ago (1 children)

what about this square, it does not have an inverse

1 1 1
1 1 1
1 1 1

[–] [email protected] 1 points 3 days ago

That magic square would be called trivial, since it contains the same entry multiple times.

exists (i.e. every non-trivial magic square has an inverse)