Question

Are [[9,7],[4,3]] and [[-3,7],[4,-9]] inverses?

Answer 1

After calculating the product of matrices [[9,7],[4,3]] and [[-3,7],[4,-9]], we find that the result is the identity matrix, indicating that these two matrices are indeed inverses of each other.

Step-by-step explanation:

To determine if the matrices [[9,7],[4,3]] and [[-3,7],[4,-9]] are inverses, we can calculate the product of these two matrices. If the result is the identity matrix, then they are indeed inverses.

Let's denote the matrices as A and B respectively:

Matrix A = [[9,7],[4,3]]
Matrix B = [[-3,7],[4,-9]]

Now let's find their product A * B:

The product is a new matrix where:

• The entry in the first row, first column is (9*-3) + (7*4) = -27 + 28 = 1
• The entry in the first row, second column is (9*7) + (7*-9) = 63 - 63 = 0
• The entry in the second row, first column is (4*-3) + (3*4) = -12 + 12 = 0
• The entry in the second row, second column is (4*7) + (3*-9) = 28 - 27 = 1

So, A * B results in:

[[1, 0], [0, 1]]

This is indeed the identity matrix, which means that matrices A and B are inverse matrices.