A=1/15(3 -13 8, 12 -7 2, -12 17 -7), B=(1 3 2, 4 5 6, 8 7 9), Multiply matrix A with B and also B with A

Sure, let's start by defining the matrices A and B:

Matrix A = 1/15 * [3 -13 8; 12 -7 2; -12 17 -7] Matrix B = [1 3 2; 4 5 6; 8 7 9]

Step 1: Multiply matrix A with matrix B (AB):

To multiply two matrices, we take each row from the first matrix and multiply it element-wise with each column of the second matrix, then sum the results. This gives us the corresponding element in the resulting matrix.

AB = A * B = 1/15 * [3 -13 8; 12 -7 2; -12 17 -7] * [1 3 2; 4 5 6; 8 7 9]

The first element of the resulting matrix is (1/15) * (31 + -134 + 8*8) = 1 The process is repeated for the rest of the elements in the resulting matrix.

So, AB = [1 0 0; 0 1 0; 0 0 1]

Step 2: Multiply matrix B with matrix A (BA):

Similarly, we multiply each row of matrix B with each column of matrix A:

BA = B * A = [1 3 2; 4 5 6; 8 7 9] * 1/15 * [3 -13 8; 12 -7 2; -12 17 -7]

The first element of the resulting matrix is (1/15) * (13 + 3(-13) + 2*8) = 1 The process is repeated for the rest of the elements in the resulting matrix.

So, BA = [1 0 0; 0 1 0; 0 0 1]

As we can see, both AB and BA are identity matrices. Therefore, we can conclude that A and B are inverses of each other.