I watched https://www.youtube.com/watch?v=Ip3X9LOh2dk to understand determinant of matrices, and understood the concept of how it is used to measure the area scaled using the transformation. Lets take a 2D matrix, say.,
[[2, 1], [3, 2]] where i vector = [2, 1] and j vector = [3, 2], the determinant turns out to be 1. Essentially, it captures the new area after the transformation. Now in the 2D space, we can measure the area by base * height. Which means if I consider i vector as my base and j vector as my height and I apply L2 norm to find the length of i and j vectors, and mulitply the L2 norm of these vectors, it should have also given the determinant which is not the case. Am I missing anything? Why would determinant not match my area computation using L2 norm?
Also, I am aware that using L2 norm doesn't capture the flip of space, where determinant would have given a negative result