The discussion confirms that the inverse of an invertible upper triangular matrix A is also an upper triangular matrix. This is established through the examination of specific examples, such as the matrix A = \begin{bmatrix} 1&1\\1&-1 \end{bmatrix}, which is invertible but not upper triangular. The inverse A^{-1} = \begin{bmatrix} 1/2&1/2\\1/2&-1/2 \end{bmatrix} demonstrates that the properties of upper triangular matrices hold true for their inverses, reinforcing the concept that the structure is preserved under inversion.
PREREQUISITESStudents and educators in linear algebra, mathematicians exploring matrix properties, and anyone interested in understanding the implications of matrix inversion on upper triangular matrices.
topgear said:Homework Statement
Show that if A is an invertible upper triangular matrix, then A^-1 is also an upper triangular matrix
Homework Equations
The Attempt at a Solution
The inverse of something just flips the main diagonal and leaves everything else where is was just changing the signs. How do I say this in math language.