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Mathematics

For two matrices A and B both of the same order, which of the following is always true :

  1. (A + B)2 = A2 + 2AB + B2

  2. (A - B)2 = A2 - 2AB + B2

  3. A × B = B × A

  4. A × (B + A) = A × B + A2

Matrices

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Answer

The Distributive Property of Matrices states that:

A(B + C) = AB + AC

where order of A is m x n and order of B and C is n x r.

∴ A x (B + A) = A x B + A2

Hence, Option 4 is the correct option.

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