Question

determine values of y if the matrix has no inverse

{2y² 2}

{1 0}

Answer 1

A matrix has no inverse if and only if its determinant is 0.

$$\det A=\begin{vmatrix} 2y^2 & 2\\ 1 & 0 \end{vmatrix}=-2\not=0, y\in \R$$

The matrix $\begin{pmatrix} 2y^2 & 2 \\ 1 & 0 \end{pmatrix}$ has inverse for $y\in \R.$

Therefore there are no values of $y$ for which the matrix $\begin{pmatrix} 2y^2 & 2 \\ 1 & 0 \end{pmatrix}$ has no inverse.