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And so on for the definitions of P_{312}, P_{321} P_{213} and P_{132}. We can ask how many row interchanges it takes to obtain a specific permutation matrix from the identity matrix. Of course, P_{123} requires zero row interchanges.
The Remarkable Relationship between the Levi-Civita Symbol and the Kronecker Delta | Deep Dive Maths
And so on for the definitions of P_{312}, P_{321} P_{213} and P_{132}. We can ask how many row interchanges it takes to obtain a specific permutation matrix from the identity matrix. Of course, P_{123} requires zero row interchanges.
The Remarkable Relationship between the Levi-Civita Symbol and the Kronecker Delta | Deep Dive Maths