Given A = [[1, 2], [3, 4]] and B = [[2, 0], [-1, 5]], find AB.

Step 1: Check that multiplication is possible.

A is a 2 × 2 matrix and B is a 2 × 2 matrix.

The number of columns of A equals the number of rows of B, so AB is defined and will be a 2 × 2 matrix.

Step 2: Find the entry in row 1, column 1.

Multiply row 1 of A by column 1 of B:

(1)(2) + (2)(-1) = 2 - 2 = 0

Step 3: Find the entry in row 1, column 2.

(1)(0) + (2)(5) = 0 + 10 = 10

Step 4: Find the entry in row 2, column 1.

(3)(2) + (4)(-1) = 6 - 4 = 2

Step 5: Find the entry in row 2, column 2.

(3)(0) + (4)(5) = 0 + 20 = 20

Step 6: Assemble the product matrix.

AB = [[0, 10], [2, 20]]

Therefore, AB = [[0, 10], [2, 20]].