CBSE 2025, Set 2

Question

Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify $4AB+3(AB+BA)-4BA,$ where $A$ and $B$ are both matrices of order $2	imes2$. It is known that $A
e B
e I$ and $A^{-1}
e B$. 
Their answers are given as:
Abhay : $6AB$
Bina : $7AB-BA$
Chhaya : $8AB$
Devesh : $7BA-AB$
Who answered it correctly? A). Abhay B). Bina C). Chhaya D). Devesh

Edvaya · Accepted Answer

The correct answer is Bina. **Solution:**

Let's simplify the given matrix expression using the distributive property of matrix multiplication:
$$E = 4AB + 3(AB + BA) - 4BA$$
$$E = 4AB + 3AB + 3BA - 4BA$$

Combine the like terms (keeping in mind that matrix multiplication is generally not commutative, meaning $AB 
e BA$ unless specified otherwise, which is not the case here):
$$E = (4AB + 3AB) + (3BA - 4BA)$$
$$E = 7AB - BA$$

Comparing this simplified result with the friends' answers, we see that Bina's answer matches perfectly.

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