Exercise 2.3.19

Answers

PQ = [\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}] .

In the opposite order, two row exchanges give

QP = [\begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix}]

$P^{2} = I .$ $If$ M $exchangesrows 2 and 3 then$ M^2=I $(also$ ${(- M)}^{2} = I) .$ There are many square roots of $I :$ Any matrix

M = [\begin{matrix} a & b \\ c & - a \end{matrix}]

has $M^{2} = I$ if $a^{2} + bc = 1$ .

mathchakra

2021-11-20 15:19