A determinant is defined for square matrices only.
To find the determinant of the matrix you need to:
To calculate the sign for the product of the n-tuple, arrange the elements in row order. Swap the elements, two at a time, to get them in column order. If the number of swaps required is even then the product is assigned a positive sign, and if odd then a negative sign.
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The determinant function is only defined for an nxn (i.e. square) matrix. So by definition of the determinant it would not exist for a 2x3 matrix.
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No.
A single math equation does not have a determinant. A system of equations (3x3 , 4x4, etc.) will have a determinant. You can find a determinant of a system by converting the system into a corresponding matrix and finding its determinant.