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Q: If A and B are n x n matrices, AB = -BA, and n is odd, show that either A or B has no inverse.

I know that we have to show that either det A is 0 or det B is 0, but I have no clue how to show it with the given information.

Q: If A^k = 0 for some k >= 1, show that A is not invertible.

Again, same problem. Any help would be great, thanks.