https://file.aiquickdraw.com/mathbot/file/17267935628738kl66129.jpg

The image presents a matrix problem in Indonesian that reads:

"Jika \( A = \begin{bmatrix} 2 & 1 \\ 0 & 2 \end{bmatrix} \), maka \( A^2 - A = \) ?"

In English, this translates to:

"If \( A = \begin{bmatrix} 2 & 1 \\ 0 & 2 \end{bmatrix} \), then \( A^2 - A = \) ?"

### Step 1: Calculate \( A^2 \)
We need to square the matrix \( A \), which means multiplying \( A \) by itself:

\[
A^2 = A \times A = \begin{bmatrix} 2 & 1 \\ 0 & 2 \end{bmatrix} \times \begin{bmatrix} 2 & 1 \\ 0 & 2 \end{bmatrix}
\]

\[
A^2 = \begin{bmatrix} (2 \times 2) + (1 \times 0) & (2 \times 1) + (1 \times 2) \\ (0 \times 2) + (2 \times 0) & (0 \times 1) + (2 \times 2) \end{bmatrix}
= \begin{bmatrix} 4 & 4 \\ 0 & 4 \end{bmatrix}
\]

### Step 2: Subtract \( A \) from \( A^2 \)
Now subtract \( A \) from \( A^2 \):

\[
A^2 - A = \begin{bmatrix} 4 & 4 \\ 0 & 4 \end{bmatrix} - \begin{bmatrix} 2 & 1 \\ 0 & 2 \end{bmatrix}
\]

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

Thus, the result is:

\[
A^2 - A = \begin{bmatrix} 2 & 3 \\ 0 & 2 \end{bmatrix}
\]

Would you like further explanation or any additional details?

### Related Questions:
1. How do you determine if a matrix is invertible?
2. What is the determinant of matrix \( A \)?
3. How would the calculation change if \( A \) were a 3x3 matrix?
4. What is the trace of a matrix, and how is it calculated for \( A \)?
5. What is the characteristic polynomial of matrix \( A \)?

### Tip:
Matrix multiplication is not commutative, meaning \( A \times B \neq B \times A \) in most cases, so the order of operations matters!

Jika A = [[2, 1], [0, 2]], maka A^2 - A = ?

Solve the matrix problem where A = [[2, 1], [0, 2]] by finding A^2 - A. This problem involves key concepts of matrix multiplication and subtraction, suitable for undergraduate students learning linear algebra.

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