Find the inverse of the matrix A= [2  1] 

To find the inverse of a 2x2 matrix, the matrix must be of the form:

\[
A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}
\]

The formula for the inverse \( A^{-1} \) is:

\[
A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}
\]

Given matrix \( A = \begin{bmatrix} 2 & 1 \end{bmatrix} \), it is not a square matrix (it's actually 1x2), making it non-invertible. For a matrix to have an inverse, it must be a square matrix (like 2x2 or 3x3).

Please provide the complete matrix if you intended a different size.

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### Follow-up Questions:
1. What are the conditions for a matrix to be invertible?
2. How do you find the inverse of a 3x3 matrix?
3. What is the determinant and why is it important for finding inverses?
4. Can non-square matrices be "inverted" using a different method?
5. How can we solve a system of linear equations using matrix inverses?

**Tip:** The determinant must be non-zero for a matrix to be invertible.

Discover why the matrix A = [2 1] is non-invertible due to its dimensions and learn the conditions for a matrix to have an inverse. This problem introduces key concepts in linear algebra, including matrix inversion and determinants, suitable for Grades 10-12.

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