7. If
what is the determinant of S-1 ?
| A. -2 | B. -1/2 | C. 1/4 | D. 1/2 | E. 2 |
Solution The answer is D.
This problem uses the theorem that det(AB) = det(A)det(B).
Thus, since SS-1 = I, where I is the identity matrix,
and since det(I) = 1 we have
Consequently, det(S-1) = 1/det(S).
Next, expanding by minors along the first row
Consequently, det(S-1) = 1/2.