First slide

Applications of determinant

Question

If A and B are two invertible matrices of the same order, then adj(AB) is equal to

Moderate

A

adj(B) adj(A)
B

$| B | | A | B^{- 1} A^{- 1}$
C

$| B | | A | A^{- 1} B^{- 1}$
D

$| A | | B | (AB)^{- 1}$

Solution

$u s e t h e p r o p e r t i e s a d j (A B) = a d j B . a d j A a n d a d j A = |A| A^{- 1}$

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