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A determinant is defined for square matrices only.

To find the determinant of the matrix you need to:

  • find all n-tuples of elements of the matrix such that each row and each column of the matrix is represented.
  • calculate the product of the elements.
  • calculate the sign for that term. To see how this is done, see below.
  • calculate the sum of the signed products: that is the determinant.

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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Q: What is the determinant of a matrix?
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