Example of matrices with eigen values $\lambda=\sqrt{t}$

Question

I'm looking for an example of 2x2 matrices $A$, $B$ such that for all $t\in\mathbb{R}$ the matrix $$C = A+tB$$ has eigenvalues $\lambda_{1,2}=\pm\sqrt{t}$, I've tried but I got always $\lambda_{1,2}=\pm t$

Answer 1

Consider \begin{align} M = \begin{bmatrix} 0 & 1\\ t & 0 \end{bmatrix} = \begin{bmatrix} 0 & 1\\ 0 & 0 \end{bmatrix}+ t \begin{bmatrix} 0 & 0\\ 1 & 0 \end{bmatrix}. \end{align}