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For any two matrices A and B, we have:

For any two matrices A and B, we have: Correct Answer None of these.

Concept:

Properties of matrix multiplication:

  • The commutative property of multiplication DOES NOT NECESSARILY HOLD!

    AB ≠ BA

    If AB = BA, then we say that A and B commute.

  • Associative property:

    (AB)C = A(BC)

  • Distributive property:

    A(B + C) = AB + AC

  • Multiplicative identity:

    IA = AI

  • Multiplication by the zero (null) matrix:

    OA = O

  • The product of an m×n matrix and an n×k matrix is an m×k matrix.

 

Calculation:

From the properties of the multiplication of matrices, we know that the commutative property of multiplication DOES NOT NECESSARILY HOLD!

Hence, the correct answer option is None of these.

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