Representations

Well, for those who have no knowledge of matrices, here's a challenge I have for you; given that the rules of 2x2 matrix mutliplication are summarised as such:


Can you find me a 2x2 matrix, such that when it's multiplied by itself, yields:


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:


And another would be:


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.