Question

The value of the determinant 

is: 
 

• A. $-2$
• B. $2$
• C. $-5$
• D. $5$

Hint:

For any $2 \times 2$ determinant, always remember the shortcut formula:
{(Top-left × Bottom-right) − (Top-right × Bottom-left)}.

Answer 1

The Correct Option is A

Step 1: Determinant rule for a 2 × 2 matrix. 
For any matrix of the form

\[ \begin{vmatrix} a & b \\ c & d \end{vmatrix} \]

the determinant is found using:

\[ ad - bc \]

Step 2: Read the values from the matrix.
From the given determinant:

\[ \begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix} \]

we identify:

\[ a = 1,\quad b = 2,\quad c = 3,\quad d = 4 \]

Step 3: Apply the determinant formula.
Substitute the values into \(ad - bc\):

\[ (1 \times 4) - (2 \times 3) \]

Step 4: Calculate the result.
 

\[ 4 - 6 = -2 \]

Step 5: Final result.
The determinant of the given matrix is:

\[ \boxed{-2} \]