This is one of my favorite theorems ever. A large part of this is because of the sense of joy I got when I figured out the proof on a midterm exam in my first-ever undergrad linear algebra course at @UCSanDiego. 
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yes such a great feeling
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Put more intuitively: if do an operation which squishes something by some amount, then the inverse operation stretches the thing by that same amount.
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I think this should be taught as one of the *defining* features of the determinant. That and the fact that det(AB)=det(A)det(B) gives a much more intuitive idea of what a determinant *is*. The silly rule for calculating them should be introduced as a consequence. Geometry is good
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......it obeys a modified version of the yeet principle
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I think it was none other than Don Knuth who said that on first reading every bit of mathematics should be replaceable by "blah". He's obviously installed some sort of bot on my twitter feed.pic.twitter.com/sIwfMRhA7n
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And true for any whole power of A!
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