Show that if A is a 2 × 2 matrix such that AB = BA

Chapter 2, Problem 39E

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QUESTION:

Show that if A is a 2 × 2 matrix such that AB = BA whenever B is a 2 × 2 matrix, then A = cI. where c is a real number and I is the 2 × 2 identity matrix.

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QUESTION:

Show that if A is a 2 × 2 matrix such that AB = BA whenever B is a 2 × 2 matrix, then A = cI. where c is a real number and I is the 2 × 2 identity matrix.

ANSWER:

SOLUTIONStep 1In this problem, we are asked to show that the matrix whenever AB=BA.

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