Let A, B, C, D be matrices of order 2 with elements over field F.
Suppose M is block-matrix that in her first row are A and B and in second row C and D.
M is matrix of order 4.
Is det(M) = det(A)*det(D) - det(B)*det(C) ?
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I think it's not. Let , , and .
We have so but
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