MathDB
matrix inverse problem

Source: VTRMC 2013 P6

May 12, 2021
linear algebramatrix

Problem Statement

Let \begin{align*}X&=\begin{pmatrix}7&8&9\\8&-9&-7\\-7&-7&9\end{pmatrix}\\Y&=\begin{pmatrix}9&8&-9\\8&-7&7\\7&9&8\end{pmatrix}.\end{align*}Let A=Y−1XA=Y^{-1}X and let BB be the inverse of X−1+A−1X^{-1}+A^{-1}. Find a matrix MM such that M2=XY−BYM^2=XY-BY (you may assume that AA and X−1+A−1X^{-1}+A^{-1} are invertible).
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