For a 2 × 2 matrix [[a, b], [c, d]], which expression represents its inverse when ad - bc is nonzero?
Correct answer: B. 1/(ad-bc) [[d, -b], [-c, a]]
- A. 1/(ad-bc) [[a, -b], [-c, d]]
- B. 1/(ad-bc) [[d, -b], [-c, a]]
- C. 1/(ad+bc) [[d, b], [c, a]]
- D. 1/(ad-bc) [[-d, b], [c, -a]]
Explanation
The inverse is found by interchanging a and d, changing the signs of b and c, and dividing by the determinant ad - bc. The inverse exists only when this determinant is nonzero.
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