Question

For which values of a does ????3a 2a − 6
6a 4a − 12
???? have an inverse matrix?

Answer 1

The matrix does not have an inverse.

Explanation:

`A=\begin{bmatrix}3a & 2a-6\\ 6a & 4a-12\end{bmatrix}`

`det\ A=3a(4a-12)-6a(2a-6)\\\Rightarrow det\ A=12a^2-36a-(12a^2-36a)\\\Rightarrow det\ A=12a^2-36a-12a^2+36a\\\Rightarrow det\ A=0`

Since the determinant of the matrix is zero it is called a singular matrix.

Singular matrices do not have an inverse.

Hence, the matrix does not have an inverse.