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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- Jan 20th 2010, 11:36 AMAlso sprach ZarathustraBlock matrices and determinant.
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) ? - Jan 20th 2010, 01:41 PMgirdav
I think it's not. Let , , and .

We have so but