![](http://2.bp.blogspot.com/_ZP-v807e_-A/SiFcMxc3wKI/AAAAAAAABCM/YcjpM74B4Mc/s400/mat2.jpg)
Can you find me a 2x2 matrix, such that when it's multiplied by itself, yields:
![](http://3.bp.blogspot.com/_ZP-v807e_-A/SiFcRSEWPiI/AAAAAAAABCU/buVe0oto4rY/s400/mat1.jpg)
There's about 10000000000000000000000000000000000 such matrices by the way. So if you can find 1, and you think you're smart, think again. Haha.
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Well, even though this post has been here for the longest time, it seems that no one has ventured beyond perfunctory reading, so I guess I'll just carry on.
One possible matrix would be:
![](http://4.bp.blogspot.com/_ZP-v807e_-A/Sj8JZuXoCdI/AAAAAAAABDU/8iAwK3mdDKw/s400/gg.jpg)
And another would be:
![](http://2.bp.blogspot.com/_ZP-v807e_-A/Sj8JVtWm2nI/AAAAAAAABDE/W2GywacMs7c/s400/aa.jpg)
There's actually a pattern: the number in the upper left and lower right positions are the same! But of course, you'd need the right combination. Heh. Can you find any more? There's probably a million more of these, haha.