Consider A= pmatrix 1 & 2 & 0 0 & 1 & 1 0 & 0 & 1 pmatrix , B= pmatrix 1 & -2 & k 0 &…

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Consider

A=\begin{pmatrix}1 & 2 & 0\\ 0 & 1 & 1\\ 0 & 0 & 1\end{pmatrix},\quad B=\begin{pmatrix}1 & -2 & k\\ 0 & 1 & m\\ 0 & 0 & 1\end{pmatrix}.

AB=I_3

and

BA=I_3

, determine the values of

k

and

m