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Chapter 7: Q26E (page 383)

TRUE OR FALSE

If two n x nmatrices A and B are diagonalizable, then AB must be diagonalizable as well.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Define Diagonalizable matrix

Any square matrix of order n is said to be diagonalizable when the matrix has n distinct eigenvalues.

02

Explanation

For example, consider the matrices,

A=1200,B=0001

Both matrices are clearly diagonalizable because both have distinct eigenvalues. However,

AB=0200

Which is not diagonalizable, because it has only one eigenvalue 0, with multiplicity 2.

Hence, the given statement is false.

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Most popular questions from this chapter

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[04-14]
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