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