Example 1 · level 1
A = [−4, 7; 3, 6]. Find the entry in row 2, column 2 of adj A.
Show solution
- adj A = [d, −b; −c, a] = [6, −7; −3, −4].
- Row 2, column 2: −4.
Answer: -4
CLASS 12 MATHS · DETERMINANTS
Adjoint and inverse of a 2 × 2 matrix
For A = [a, b; c, d], adj A = [d, −b; −c, a] and A⁻¹ = (1/|A|) adj A, provided |A| = ad − bc ≠ 0.
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Worked examples
Example 2 · level 2
A = [−2, 3; 4, 6]. Find the entry in row 2, column 1 of A⁻¹. (Give a fraction if needed.)
Show solution
- |A| = −24.
- adj A = [6, −3; −4, −2].
- Entry of A⁻¹ = −4 ÷ (−24) = 1/6.
Answer: 1/6
Example 3 · level 3
Solve by the matrix method: 6x + 6y = −18, 6x − 3y = −36. Find y.
Show solution
- |A| = −54 ≠ 0, so a unique solution exists.
- x = (−3 × −18 + −6 × −36) ÷ −54 = −5.
- y = (−6 × −18 + 6 × −36) ÷ −54 = 2.
Answer: 2