Question

Let a and b be 3 Ã 3 matrices with det(a) = 4 and det(b) = 5. find the value of (a) det(ab)

Answer 1

(a) |AB| = |A| |B| = -1 * 2 = -2.

(b) |B^5| = |B|^5 = 2^5 = 32.

(c) Since A is 4 x 4,
|2A| = 2^4 * |A| = 16 * -1 = -16.

(d) Since determinants are invariant under transposition,
|A^t A| = |A^t| |A| = |A| |A| = (-1)(-1) = 1.

(e) |B^(-1) AB| = |B^(-1)| |A| |B|
.....................= (1/|B|) |A| |B|
.....................= |A|
.....................= -1.

I hope this helps!