Which of the following matrices have eigen values as 1 and -1 ? (a) `[(0,1),(1,0)]` (b) `[(0,1),(1,0)]` (c) `[(1,0),(0,-1)]` (d) `[(1,0),(0,1)]`

Options

A. `[(0,1),(1,0)]`
B. `[(0, -i),(i,0)]`
C. `[(1,0),(0,-1)]`
D. `[(1,0),(0,1)]`

Explanation

To determine which of the given matrices have eigenvalues of 1 and -1, we will follow these steps for each matrix:

1. **Find the characteristic polynomial** of the matrix using the formula:
\[ \text{det}(A - \lambda I) = 0 \]
where \( A \) is the matrix, \( \lambda \) is the eigenvalue, and \( I \) is the identity matrix.

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