Fewpal
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Given an example of matrices A, B and C such that AB = AC, where A is non-zero matrix, but B ≠ C.

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

Take,

Multiply 1st row of matrix A by matching members of 1st 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

Multiply 1st row of matrix A by matching members of 1st 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

Clearly, AB = AC.

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

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