check that B is the correct inverse using R

To check if B is the correct inverse of A, we can multiply A and B together. If the result is the identity matrix, then B is indeed the inverse of A.

In R, you can do this using the following steps:

Step 1: Define the matrices A and B.

A <- matrix(c(13, 11, 9, 12, 11, 6, 3, 10, 17, 8, 10, 9, 33, 6, 1, 2), nrow=4, byrow=TRUE)
B <- solve(A)  # This will calculate the inverse of A

Step 2: Multiply A and B together.

result <- A %*% B

Step 3: Check if the result is the identity matrix.

identity_matrix <- diag(4)  # This creates a 4x4 identity matrix
is_inverse <- all(abs(result - identity_matrix) < 1e-10)  # This checks if all elements of (result - identity_matrix) are less than 1e-10

If is_inverse is TRUE, then B is the correct inverse of A. If is_inverse is FALSE, then B is not the correct inverse of A.

Please note that due to numerical precision issues, we check if the elements of (result - identity_matrix) are less than a small number (1e-10 in this case) instead of checking if they are exactly zero.