Can you help me with the problem? ### Matrix Multiplicative Identity Problem**Use the following matrix to answer the question:**\[ A = \begin{bmatrix} 1 & \frac{1}{2} \\ 0 & -2 \end{bmatrix} \]**What is the multiplicative identity of matrix A?**a. \[ \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix} \]b. \[ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \]c. \[ \begin{bmatrix} -1 & -1 \\ 0 & 2 \end{bmatrix} \]d. \[ \begin{bmatrix} -2 & -1 \\ 0 & 1 \end{bmatrix} \]e. \[ \begin{bmatrix} 1 & \frac{1}{2} \\ 0 & -\frac{1}{2} \end{bmatrix} \]**Explanation:**In this exercise, you are asked to determine the multiplicative identity that, when multiplied by matrix \( A \), results in the identity matrix \( I \), which is:\[ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \]Understanding the concept of the multiplicative identity is crucial in linear algebra for solving systems of equations, among other applications. Consider the choices above and compute the product of matrix \( A \) with each option to determine which satisfies the condition \( A \times I = I \times A = A \).

Name: Can you help me with the problem? ### Matrix Multiplicative Identity P
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: Can you help me with the problem? ### Matrix Multiplicative Identity Problem**Use the following matrix to answer the question:**\[ A = \begin{bmatrix} 1 & \frac{1}{2} \\ 0 & -2 \end{bmatrix} \]**What is the multiplicative identity of matrix A?**a. \[