How to solve
An invertible 2×2 matrix undoes itself via A⁻¹ = (1/det) [[d, −b], [−c, a]]. First ensure det = ad − bc ≠ 0; these drills ask for the (1,1) entry of that inverse as a simplified fraction.
Steps
- Compute det = ad − bc and confirm it is nonzero.
- Form (1/det) [[d, −b], [−c, a]].
- Report the (1,1) entry d/det in lowest terms.
Example
For A = [[2, 1], [1, 2]], find the (1,1) entry of A⁻¹.
- det = 2 · 2 − 1 · 1 = 3.
- A⁻¹ = (1/3) [[2, −1], [−1, 2]].
- (1,1) entry = 2/3.
Answer: 2/3
How to type answers
- Enter a simplified fraction like 3/5 or -1/2
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