[tex] det \left[\left(\begin{array}{cc}1&2\\4&8\end{array}\right) + \left(\begin{array}{cc}x&0\\0&x\end{array}\right)\right] = det \left(\begin{array}{cc}1+x&2\\4&8+x\end{array}\right)[/tex]
=> (1+x)(8+x) - 8 = 0
8 + 9x + x^2 - 8 =0
x^2 + 9x = 0
x(x+9)=0
=> x={0,-9}
