Question

Determine if the matrices are inverses of each other by multiplying them.

A) They are inverses
B) They are not inverses
C) Inconclusive
D) Matrix multiplication is not defined for these matrices

Answer 1

The matrices are inverses of each other, so the correct option is (A) They are inverses.

Step-by-step explanation:

Given matrices A and B:

A = [3 1] B = [4 -1]

[2 4] [-2 3]

Multiply matrices A and B:

AB = [3*4 + 1*(-2) 3*(-1) + 1*3]

[2*4 + 4*(-2) 2*(-1) + 4*3]

= [12 - 2 -3 + 3]

[8 - 8 -2 + 12]

= [10 0]

[0 10]

The result is the identity matrix I:

I = [1 0]

[0 1]

Since AB equals the identity matrix I, matrices A and B are inverses of each other.

Therefore, the correct answer is (A) They are inverses.