# Find the values of α such that the following matrix is invertible

I have the following matrix

$$\begin{pmatrix} 1 &-1 &α-1\\1 &1 &1\\ 2α & 2 & 4 \end{pmatrix}$$

I only have to set the determinant of this matrix to $$0$$. Then find values of $$α$$ when the determinant equals to $$0$$, and the values of $$\alpha$$ are correct?

• The matrix is invertible when the determinant is not zero. So yes, find the values of $a$ for which the determinant is zero and that will give you the values for which it is not zero. – Mark Oct 11 at 12:14
• There are several questions of this type already here on this site, e,g, here. Please look for duplicates before posting. – Dietrich Burde Oct 11 at 12:40