Question

If the matrix \[ A= \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \] then the value of $|A|$ is:

• A. $-2$
• B. $2$
• C. $10$
• D. $-10$

Hint:

For a $2\times2$ matrix, determinant is always: \[ ad-bc \] Multiply the principal diagonal first and then subtract the product of the other diagonal.

Answer 1

The Correct Option is A

Concept: For a matrix of order $2\times2$: \[ A= \begin{bmatrix} a & b \\ c & d \end{bmatrix} \] its determinant is: \[ |A|=ad-bc \] This is one of the most fundamental formulas in matrices and determinants.

Step 1: Identify the matrix elements.
Given: \[ A= \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \] Comparing with the standard form: \[ a=1,\qquad b=2,\qquad c=3,\qquad d=4 \]

Step 2: Apply the determinant formula.
Using: \[ |A|=ad-bc \] Substitute the values: \[ |A|=(1)(4)-(2)(3) \] \[ |A|=4-6 \] \[ |A|=-2 \] Therefore, \[ \boxed{-2} \]