Question

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

Answer 1

option C

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