Let A = Anxn be an invertible matrix. Which of the following statements is not true? %3D O There exists a matrix B such that AB = BA= I O N(A) = {0} O For each b E R", Ax = b has a unique solution %3D O det A = 0 O rank(A=n

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 21E: Suppose that A is an invertible matrix over and O is a zero matrix. Prove that if AX=O, then X=O.
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Let A = Anxn be an invertible matrix. Which of the following statements is not true?
O There exists a matrix B such that AB = BA=I
O N(A) = {0}
O For each b E R", Ax= b has a unique solution
O det A = 0
O rank(A= n
Transcribed Image Text:Let A = Anxn be an invertible matrix. Which of the following statements is not true? O There exists a matrix B such that AB = BA=I O N(A) = {0} O For each b E R", Ax= b has a unique solution O det A = 0 O rank(A= n
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