Evaluate : `|{:(2,4),(-1,2):}|`

Answer

To evaluate the determinant of the given 2x2 matrix \(\begin{pmatrix} 2 & 4 \\ -1 & 2 \end{pmatrix}\), we will follow these steps:

### Step 1: Write the determinant
We start by writing the determinant in the standard form:
\[ |A| = \begin{vmatrix} 2 & 4 \\ -1 & 2 \end{vmatrix} \]

### Step 2: Apply the determinant formula for a 2x2 matrix
The formula for the determinant of a 2x2 matrix \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\) is given by:
\[ |A| = ad - bc \]
In our case, \(a = 2\), \(b = 4\), \(c = -1\), and \(d = 2\).

### Step 3: Substitute the values into the formula
Substituting the values into the determinant formula:
\[ |A| = (2)(2) - (4)(-1) \]

### Step 4: Calculate the products
Now we calculate the products:
\[ |A| = 4 - (-4) \]

### Step 5: Simplify the expression
Since subtracting a negative number is the same as adding a positive number, we have:
\[ |A| = 4 + 4 \]

### Step 6: Final calculation
Now, we can perform the final addition:
\[ |A| = 8 \]

Thus, the value of the determinant is:
\[ \boxed{8} \]

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