If A is of order 3 × 2 and B is of order 2 × 3, then BA is of order:

If A = [[2, 1], [0, 3]] and I is the 2 × 2 identity matrix, find AI and IA and state what this shows.

Give an example to show that matrix multiplication is not commutative.

If A = [[3, 1], [0, 2]], find A².

Find the product [[1, 2], [3, 4]] × [[2, 0], [1, 3]].

Find x and y if [[x, 3], [2, y]] = [[4, 3], [2, 5]].

If A = [[1, 2], [3, 4]], find its transpose and state its order.