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True or false: Every elementary permutation matrix satisfies P2 = 1.

User Pieter
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Final answer:

The statement is false. Not every elementary permutation matrix satisfies P2 = 1.

Step-by-step explanation:

The statement is false. Not every elementary permutation matrix satisfies P2 = 1.

An elementary permutation matrix is a square matrix obtained by interchanging two rows (or columns) of the identity matrix. Let's take an example:

Consider the matrix P = | 0 1 |, which is obtained by interchanging the first and second rows of the 2x2 identity matrix.

To find P2, we need to multiply P by itself:

P x P = | 0 1 | x | 0 1 | = | 0 1 | x | 0 1 | = | 1 0 |.

Therefore, P2 = | 1 0 | ≠ 1, so the statement is false.

User Codaniel
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