= 11. Consider the matrix equation X5 : I2, where I2 is the 2 × 2 identity matrix. Over each of the following fields, decide whether the above equation has a solution that is not I₂ itself. Justify your answers. a. Q b. R c. C d. Zp, the finite field of p elements, where p is a prime number.

= 11. Consider the matrix equation X5 : I2, where I2 is the 2 × 2 identity matrix. Over each of the following fields, decide whether the above equation has a solution that is not I₂ itself. Justify your answers. a. Q b. R c. C d. Zp, the finite field of p elements, where p is a prime number.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 63EQ

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Question

11. Consider the matrix equation X5 = I2, where I2 is the 2 × 2
identity matrix. Over each of the following fields, decide whether the
above equation has a solution that is not I₂ itself. Justify your answers.
a. Q
b. R
c. C
d. Zp, the finite field of p elements, where p is a prime number.

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