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Consider the following statements: Statement 1: For the diagonal matrix A = [[a, 0, 0],[0, b, 0],[0, 0, c]], its inverse is A⁻¹ = [[1/a, 0, 0],[0, 1/b, 0],[0, 0, 1/c]]. Statement 2: The inverse of any diagonal matrix is also a diagonal matrix.

1. Statement 1 is true, Statement 2 is true, and Statement 2 correctly explains Statement 1.
2. Statement 1 is true, Statement 2 is true, but Statement 2 does not correctly explain Statement 1.
3. Statement 1 is false, Statement 2 is true.
4. Statement 1 is true, Statement 2 is false.

Correct answer: Statement 1 is true, Statement 2 is true, but Statement 2 does not correctly explain Statement 1.

Solution

Statement 1 is accurate because the inverse of a diagonal matrix is obtained by taking the reciprocal of its diagonal elements, which is correctly represented. Statement 2 is also true since the inverse of any diagonal matrix remains diagonal, but it does not specifically explain why the inverse in Statement 1 is valid.

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