Let A and B be two non-singular, square matrices of same order, and
A. (AB)–1 = B–1.A–1
B. (A + B)–1 = B–1 + A–1
C. adj. A = |A|.A–1
D. det(A–1) = [det A]–1
Choose the correct answer from the options given below
Answer & explanation
Correct answer: option 4
A. (AB)–1 = B–1.A–1
B. (A + B)–1 ≠ B–1 + A–1
C. adj. A = |A|1
$adj(A) = |A|\frac{1}{A}⇒|A|.A^{-1}$
D. det(A–1) = [det A]–1
∴ A, C, & D options are correct.
So option 4th is correct.