# Re: [xmca] a minus times a plus

```matrix operations are non-commutative in general.  oooops!
OK, point taken about "who is going to educate the educator"

nevertheless, i thought perhaps we can use insights about the
determinants to help us design explanation aids for the child.
the (+/- sign of) determinants determine the clockwise /
anti-clockwise sense changes.  we can draw x- and y- with 4
quadrants.  put a two-row by three-column block of smiley faces,
put an arrowhead to the left end of the smile (2×3) so it seems
to indicate a clockwise rotation.  reflect this in the y-axis,
you get (-2×3) and the six smileys turn anti-clockwise (-6).
reflect this in the x-axis, you get (-2×-3) and you see six
smileys turn clockwise (+6).  reflect this in the y-axis,
you get (2×-3) and you see six smileys turn anti-clockwise (-6).

Foo Keong
NIE, Singapore

2009/4/29 Andy Blunden <ablunden@mira.net>:
> But Foo Keong,
> Are you seriously suggesting that Mike should use these observation about
> the commutativity of matrix operations and their determinants to teach his
> granddaughter why -x-=+?
> I suspect that Mike doesn't understand it himself.
> Who is to educate the educator?
> Andy
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