Are matrices A and B inverses
A=[[-5,-18],[2,7]] and B=[[7,18],[-2,-5]]
To determine if two matrices are inverses, we can multiply them together and see if the result is the identity matrix.
Using matrix multiplication, we find that:
AB = [[-5*-2 + -18*-5, -5*7 + -18*-2], [2*-2 + 7*-5, 2*7 + 7*-2]]
= [[10 + 90, -35 + 36], [-4 - 35, 14 - 14]]
= [[100, 1], [-39, 0]]
The resulting matrix is not the identity matrix, so matrices A and B are not inverses of each other.
To determine whether matrices A and B are inverses, we need to multiply them together and check if the result is the identity matrix.
1. Multiply matrix A by matrix B:
AB = A * B
The resulting matrix will be:
AB = [[(-5*-5) + (-18*-2), (-5*18) + (-18*-5)],
[(2*-5) + (7*-2), (2*18) + (7*-5)]]
Simplifying the multiplication, we get:
AB = [[103, -135],
[-24, 61]]
2. Check if AB is equal to the identity matrix.
The identity matrix is a special square matrix where all the elements on the main diagonal are 1, and all the other elements are 0.
Comparing the resulting matrix AB to the identity matrix, we find that they are not equal. Therefore, matrices A and B are not inverses of each other.
To determine if matrices A and B are inverses, we need to check if the product of A and B is the identity matrix.
Let's calculate the product of A and B:
A * B = [[-5, -18], [2, 7]] * [[7, 18], [-2, -5]]
= [[-5*7 + -18*-2, -5*18 + -18*-5], [2*7 + 7*-2, 2*18 + 7*-5]]
= [[35 + 36, -90 + 90], [14 - 14, 36 - 35]]
= [[71, 0], [0, 1]]
The result is not the identity matrix which is [[1, 0], [0, 1]], so matrices A and B are not inverses.
In summary, matrices A and B are not inverses.