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

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

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

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step-by-step explanation: