10/14/2023 0 Comments Determinant of a matrix![]() ![]() One wants the determinant function to characterize when exactly a matrix X has an inverse (it just so happens to be that X has an inverse iff det(X) != 0). Thus only square matrices can have inverses. Since AB = BA = I, this forces n = q = p = m = t, i.e. B is both a left inverse and a right inverse of A). "The" inverse of a matrix A is a matrix B such that AB = BA = I (i.e. No wonder, the determinant function (or "a determinantal function") is defined as a function from the set of all nxn (i.e square) matrices (with elements in a field F), to the field F (the determinant takes a square matrix and spits back out a number). But it says nothing about how to solve for a 3 X 2 Matrix.
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