Exercise 9.1. Let R = M2(R), the ring of 2-by-2 matrices with entries in R. (1) Show that a matrix A E R is a zero divisor if and only if det(A) = 0. (2) Show that every left zero divisor of R is also a right zero divisor of R. (This actually holds for R = Mn(R).)

Exercise 9.1. Let R = M2(R), the ring of 2-by-2 matrices with entries in R. (1) Show that a matrix A E R is a zero divisor if and only if det(A) = 0. (2) Show that every left zero divisor of R is also a right zero divisor of R. (This actually holds for R = Mn(R).)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.5: Applications

Problem 30EQ

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Question

Exercise 9.1. Let R = M2(R), the ring of 2-by-2 matrices with entries in R.
(1) Show that a matrix A E R is a zero divisor if and only if det(A) = 0.
(2) Show that every left zero divisor of R is also a right zero divisor of R.
(This actually holds for R = Mn(R).)

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