Question

Determine whether the given matrices are multiplicative inverse of each other

[3 5] and [7 -5]
[4 7] [-4 3]

Answer 1

They are multiplicative inverse of each other.

Explanation:

Two matrices are multiplicative inverses of each other if their product is the identity matrix.

Let’s multiply the two given matrices to see if their product is the identity matrix:

[3 5] * [7 -5] = [37 + 5(-4) 3*(-5) + 53] = [1 0]

[4 7] [-4 3] [47 + 7*(-4) 4*(-5) + 7*3] [0 1]

As we can see, the product of the two matrices is the identity matrix. Therefore, the given matrices are multiplicative inverses of each other.

Hope this helps!