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The problem asks to find \( A - I \), where \( A \) is a given 2x2 matrix, and \( I \) is the 2x2 identity matrix.

Given:
\[
A = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}
\]
The 2x2 identity matrix \( I \) is:
\[
I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}
\]

Now, we need to compute \( A - I \):

\[
A - I = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} - \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} = \begin{pmatrix} 2-1 & 3-0 \\ 1-0 & 4-1 \end{pmatrix} = \begin{pmatrix} 1 & 3 \\ 1 & 3 \end{pmatrix}
\]

So, \( A - I = \begin{pmatrix} 1 & 3 \\ 1 & 3 \end{pmatrix} \).

The correct answer corresponds to option **a)**.

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. How do you determine if a matrix is invertible?
2. What is the determinant of matrix \( A \)?
3. How do you calculate the trace of a matrix?
4. What is the rank of matrix \( A \)?
5. How would the result change if \( A \) were a 3x3 matrix?

**Tip:** When working with matrices, it's crucial to keep track of matrix dimensions to ensure operations like addition and multiplication are valid.

Let A = [ [2, 3], [1, 4] ] and I be the 2x2 identity matrix. What is A - I?

This page provides a step-by-step solution to the matrix subtraction problem involving a 2x2 matrix A and the 2x2 identity matrix I. Learn about matrix algebra, identity matrices, and how to perform matrix subtraction. Suitable for students in Grades 10-12.

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