Question

A, B and C are three matrices each of order 2 × 2.

Statement (1): If A × B = A × C ⇒ B = C.

Statement (2): Cancellation law is applicable in matrix multiplication.

विकल्प

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are false.

Explanation:

We know that,

Matrix multiplication does not satisfy the cancellation law.

∴ Statement 2 is false.

Thus, if A × B = A × C, we cannot conclude that B = C.

∴ Statement 1 is false.