Find |A| if `A = |(4x, 3x), (5x, 6x)|`

Answer

To find the value of the determinant |A| for the matrix \( A = \begin{pmatrix} 4x & 3x \\ 5x & 6x \end{pmatrix} \), we will follow these steps:

### Step 1: Write down 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:
\[ |A| = ad - bc \]

### Step 2: Identify the elements of the matrix
In our case, we have:
- \( a = 4x \)
- \( b = 3x \)
- \( c = 5x \)
- \( d = 6x \)

### Step 3: Substitute the values into the determinant formula
Now, substituting the identified values into the determinant formula:
\[ |A| = (4x)(6x) - (3x)(5x) \]

### Step 4: Perform the multiplication
Calculating each term:
\[ |A| = 24x^2 - 15x^2 \]

### Step 5: Simplify the expression
Now, simplify the expression:
\[ |A| = (24 - 15)x^2 = 9x^2 \]

### Final Answer
Thus, the value of the determinant |A| is:
\[ |A| = 9x^2 \]

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