We need to form matrices A, B and C such that AB = AC, where A is a non-zero matrix, but B ≠ C.

Take,

First, compute AB.

Multiply 1^st row of matrix A by matching members of 1^st column of matrix B, then sum them up.

(1, 0)(1, 2) = (1 × 1) + (0 × 2)

⇒ (1, 0)(1, 2) = 1 + 0

⇒ (1, 0)(1, 2) = 1

Similarly, let us do the same for other elements.

Now, let us compute AC.

Multiply 1^st row of matrix A by matching members of 1^st column of matrix C, then sum them up.

(1, 0)(1, 2) = (1 × 1) + (0 × 2)

⇒ (1, 0)(1, 2) = 1 + 0

⇒ (1, 0)(1, 2) = 1

Similarly, let us do the same for other elements.

Clearly, AB = AC.

Thus, we have found an example that satisfy the required criteria.