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In Exercises 9 and 10, mark each statement True or False.
Chapter 2, Problem 9E(choose chapter or problem)
In Exercises 9 and 10, mark each statement True or False. Justify each answer.a. In order for a matrix B to be the inverse of A, the equations AB = I and BA = I must both be true.b. If A and B are n × n and invertible, then A–1B–1 is the inverse of AB.c. If then A is invertible.d. If A is an invertible n × n matrix, then the equation Ax = b is consistent for each b in ?n.e. Each elementary matrix is invertible.
Questions & Answers
QUESTION:
In Exercises 9 and 10, mark each statement True or False. Justify each answer.a. In order for a matrix B to be the inverse of A, the equations AB = I and BA = I must both be true.b. If A and B are n × n and invertible, then A–1B–1 is the inverse of AB.c. If then A is invertible.d. If A is an invertible n × n matrix, then the equation Ax = b is consistent for each b in ?n.e. Each elementary matrix is invertible.
ANSWER:Solution : Step 1 : a. In order for a matrix B to be the inverse of A, the equations AB=I and BA=I must both be true.ans ; True, because B must be the inverse matrix of A.b. If A and B are n × n and invertible, then is