We know that the 2 × 2 matrix A = a b c d $ A = \left[ {\begin{array}{*{20}l} a \hfill & b \hfill \\ c \hfill & d \hfill \\ \end{array} } \right] $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315172309/e112b15c-ee8b-4102-9c2c-0d5caba3f84a/content/inline-math5_1.tif"/> is invertible if and only if the scalar ad| - bc ≠ 0. And we also learned that elementary row operations do not change invertibility of a matrix. If we regard the scalar ad bc $ \text{ad}\text{bc} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315172309/e112b15c-ee8b-4102-9c2c-0d5caba3f84a/content/inline-math5_2.tif"/> as the value of a function, called determinant det $ {\text{det }} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315172309/e112b15c-ee8b-4102-9c2c-0d5caba3f84a/content/inline-math5_3.tif"/> acting on the matrix A, we wish to know how elementary row operations will change the function value.