Question

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

Answer 1

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 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

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

Clearly, AB = AC.

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