Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are

1. $1$ and $1$
2. $1$ and $-1$
3. $j$ and $-j$
4. $pq$ and $-pq$

SOLUTION

FORMULA OF EIGEN VALUE

where A  is eign value

det(matrix)=(-p^2-q^2)

given question (p^2+q^2)=1

then put value

A^2-1=0

the A=1and -1(ans)
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