How many 4 × 4 matrices with entries from {0, 1} have odd determinant? is there a short way of finding the answer to this question or do we have to solve it by hit and trial or using lengthy methods. if there is a short formula based answer to this,then please help me with this thank you
2026-04-02 14:58:22.1775141902
odd determinants
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This is the same as asking how many $4\times 4$ matrices with coefficients in $\mathbb{Z}/2\mathbb{Z}$ have nonzero determinant.
This is a standard argument: pick a nonzero vector for the first row, pick a vector not in the span of the first vector for the second row, etc. This gives us $(2^4-2^0) (2^4-2^1) (2^4-2^2) (2^4-2^3)$ possibilities.