Matrix Determinants?

Question

Problem 1

Given matrixes A & B

Det(AB) = 18

Det(B) = 6

What is determinant of A?

Problem 2

Given matrix A

Det(A) = 5

What is the determinant of the inverse matrix of A?

Answer 1

1: Det(A)=3

2: Det(A^-1)=Det(A)=5

Answer 2

For 1)  Use the fact that det (AB) = det (A) det (B)     meaning the det (A) times det (B) should equal 18.  So, the det (A) is 3

For 2)  Use the rule that det (A^-1) = (det (A))^-1

Answer 3

Determinants are multiplicative

So Det(AB) = Det(A) * Det(B)

Det(A) = 18/6 = 3

Determinant of inverse = 1/Det(A)

Therefore Det(A inverse) = 1/5 = 0.2