Find the inverse of matrix B = [[2, 1], [5, 3]]

To find the inverse of a 2x2 matrix, you can follow these steps:

1. Calculate the determinant of the matrix. The determinant of a 2x2 matrix [[a, b], [c, d]] is given by (ad - bc). For matrix B, the determinant is (23 - 51) = 1.

2. If the determinant is zero, the matrix does not have an inverse. In this case, the determinant is not zero, so we can proceed.

3. Swap the elements of the main diagonal, so we get [[3, 1], [5, 2]].

4. Change the sign of the elements off the main diagonal, so we get [[3, -1], [-5, 2]].

5. Multiply each element by 1/determinant, so we get [[3/1, -1/1], [-5/1, 2/1]], which simplifies to [[3, -1], [-5, 2]].

So, the inverse of matrix B is [[3, -1], [-5, 2]].