We want to see which one of the given matrices has an inverse.
The correct option is:
[tex]\left[\begin{array}{ccc}6&-9\\2&1\end{array}\right][/tex]
A matrix will only have an inverse if:
- The matrix is square (same number of columns and rows).
- The determinant is not zero.
Here we have only one square matrix, the third one, so we can discard the rest.
Now we need to see if the determinant is different than zero.
Remember that the determinant in a general matrix:
[tex]\left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right][/tex]
is written as:
a₁₁*a₂₂ - a₁₂*a₂₁
In the case of the third matrix, the determinant is:
D = 6*1 - (-9)*2 = 6 - 18 = -12
So this is different than zero, meaning that the matrix has an inverse.
Then the correct option is the third matrix, counting from the top.
[tex]\left[\begin{array}{ccc}6&-9\\2&1\end{array}\right][/tex]
If you want to learn more, you can read:
https://brainly.com/question/4017205
