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Suppose that A and B are arbitarary 2×2 matirices. Is the quantity given always equal to (A+B)2 (a) A2 +2AB+C2. (b) (B+A)2(c) A(A+B)+B(A+B) (d) A2 +AB+AB+C2

Respuesta :

Answer:

option C

Step-by-step explanation:

given,

A and B are arbitrary 2×2 matrices

we need to find

        (A+B)²

 (A+B)² =  (A+B)(A+B)

 (A+B)² =  A.A + A.B + B.A + B.B

 (A+B)² =  A² + A.B + B.A + B²

Matrix multiplication does not follow multiplicative law

    AB ≠ BA

 (A+B)² =  A² + A.B + B.A + B²

now,

 (A+B)² =  A(A+B)+ B(A+B)

the correct answer is option C

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