I am so pleased and thankful for this book! Nowhere else have I been able to find a rigorous, complete and fully motivated development of the definition of a determinant (not online, not in other linear algebra textbooks of which i have 4 including the excellent text by David Lay et al as well as numerous other books). This book has equipped me to teach not only how to DO determinants and how to prove that determinants correlate with area, volume and hypervolume, but rather develops the determinant as the geometric concept of area/volume/hypervolume of a parallelepiped in n dimensions -- which also determines whether or not a nxn matrix can be inverted -- and from this all the basic properties of determinants become clear. Elsewhere the approach seems to be, "motivate" the determinant by discussing a 2x2 matrix and then define the matrix as the row or column expansion of minor submatrices -- proving from this seemingly arbitrary definition various matrix aspects which are much more naturally discussed by this book. SOME other books even point out that all the additive terms can be formed by permutations of columns to determine which factor is selected from each row of the matrix to calculate the determinant, but not really demonstrating WHY in a general sense. Although it is not easy in the sense that some of the proofs are subtle still they are quite well done, so I recommend the book for any math major, math professor, or (in my case) former math major teaching a precocious 7th grader who has already blown through algebra, trig and calculus.