Consider an invertible linear transformation T(x) = Ax from Rm to R \ with inverse L =
Chapter 2, Problem 48(choose chapter or problem)
Consider an invertible linear transformation T(x) = Ax from Rm to R \ with inverse L = T~[ from R" to Rm. In Exercise 2.2.29 we show that L is a linear transformation, so that L(y) = By for some m x n matrix B. Use the equations BA = In and AB = Im to show thatn = m. (Hint: Think about the number of solutions^ the linear systems Ax 0 and By = 5.)
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