TIFR ECE 2022 | Question: 12

Question

An $n \times n$ matrix $\mathbf{P}$ is called a Permutation Matrix if each of its $n$ columns and $n$ rows contain exactly one $1$ and $n-1 \; 0$ 's. Consider the following statements:

1. $\operatorname{det}(\mathbf{P})$ is either $+1$ or $-1$.
2. If $\lambda$ is an eigen value of $\mathbf{P}$, then $|\lambda|=1$.
3. $\mathbf{P}^{T}=\mathbf{P}^{-1}$.

Which of the following is $\text{TRUE}?$

• A. Only statement $1$ is correct
• B. Only statements $1, 2$ are correct
• C. Only statements $1,3$ are correct
• D. Only statements $2, 3$ are correct
• E. All statements $1, 2,$ and $3$ are correct