Consider the lower-triangular matrices A= pmatrix 1 & 0 & 0 2 & 1 & 0 3 & 4 & 1…

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

Consider the lower-triangular matrices

A=\begin{pmatrix}1 & 0 & 0\\ 2 & 1 & 0\\ 3 & 4 & 1\end{pmatrix},\qquad B=\begin{pmatrix}1 & 0 & 0\\ p & 1 & 0\\ q & r & 1\end{pmatrix},

where

p,\,q,\,r\in\mathbb R

and

AB=I_3

. (i) Determine the values of

p,\,q,

and

r

. (ii) For the values obtained in part (i), compute

BA

and state whether

BA=I_3

. Give a reason for your answer. (iii) Write the inverse of

A

in closed form.