If the value of |A| is 48 the possible values for x in the matrix is 4 or -2.
How to use determinant to find a value in a matrix?
The determinant of the matrix A is as follows:
|A| = 48
Therefore,
48 = (3x × 2x) - (4x × 3)
48 = 6x² - 12x
6x² - 12x - 48 = 0
3x² - 6x - 24 = 0
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x(x + 2 -4(x + 2) = 0
(x - 4)(x +2) = 0
Therefore,
x = 4 or -2
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