Question

Multiply the matrices: \[ \left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \]

• A. \( \left[ \begin{matrix} 1 & 0 \\ 0 & 4 \end{matrix} \right] \)
• B. \( \left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \)
• C. \( \left[ \begin{matrix} 1 & 2 \\ 0 & 4 \end{matrix} \right]\)
• D. \( \left[ \begin{matrix} 1 & 3 \\ 2 & 0 \end{matrix} \right] \)

Hint:

Multiplying any matrix by the identity matrix will result in the original matrix.

Answer 1

The Correct Option is B

Matrix multiplication involves taking the dot product of rows from the first matrix with columns from the second matrix. Here, the second matrix is the identity matrix: \[ \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \] Multiplying any matrix with the identity matrix will return the original matrix. Therefore, multiplying: \[ \left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] = \left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \] Thus, the correct answer is option (B).