What is the inverse of the 2x2 matrix with rows [1 2] and [3 4]?
A
[-2 1] and [1.5 -0.5]
B
[4 -2] and [-3 1]
C
[1 -2] and [-3 4]
D
Does not exist
Correct Answer: Option A — [-2 1] and [1.5 -0.5]
Explanation:
For matrix [[1 2][3 4]] det = 4-6 = -2. Inverse = (1/det)×[[d -b][-c a]] = (-1/2)×[[4 -2][-3 1]] = [[-2 1][1.5 -0.5]]. Matrix inversion is used in solving linear systems and transformations. It exists only when the determinant is non-zero and is tested in CSS PMS mathematical topics.