Class CBSE Class 12 Mathematics Matrices and Determinants Q #1681
COMPETENCY BASED
APPLY
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
Let $A=\begin{bmatrix}0&-3&4\\1&0&2\end{bmatrix}$ and $B=\begin{bmatrix}-3&0&1\\2&4&0\end{bmatrix}$. If $A + B + C = O$, then matrix C is:
(A) $\begin{bmatrix}-3&-3&5\\3&4&2\end{bmatrix}$
(B) $\begin{bmatrix}3&3&-5\\-3&-4&-2\end{bmatrix}$
(C) $\begin{bmatrix}3&3&5\\-3&-4&-2\end{bmatrix}$
(D) $\begin{bmatrix}-3&-3&-5\\3&4&2\end{bmatrix}$
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Correct Answer: B

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Detailed Solution

Step 1: Understand the Equation

Given the equation $A + B + C = O$, where $O$ is the zero matrix of the same order as $A$ and $B$ ($2 \times 3$), we need to isolate matrix $C$. By subtracting $(A + B)$ from both sides, we get: $$C = -(A + B)$$

Step 2: Calculate the Sum (A + B)

Add the corresponding elements of matrices $A$ and $B$: $$A + B = \begin{bmatrix} 0+(-3) & -3+0 & 4+1 \\ 1+2 & 0+4 & 2+0 \end{bmatrix} = \begin{bmatrix} -3 & -3 & 5 \\ 3 & 4 & 2 \end{bmatrix}$$

Step 3: Calculate C = -(A + B)

Multiply every element of the resulting matrix by $-1$: $$C = -\begin{bmatrix} -3 & -3 & 5 \\ 3 & 4 & 2 \end{bmatrix} = \begin{bmatrix} 3 & 3 & -5 \\ -3 & -4 & -2 \end{bmatrix}$$

Final Answer: Option (B)

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to utilize the properties of matrix addition and scalar multiplication to solve for an unknown matrix.
Knowledge Dimension: PROCEDURAL
Justification: The question tests the student's ability to execute a specific sequence of algebraic steps (addition followed by negation) within the domain of matrix algebra.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. This question aligns with the NCERT curriculum for Matrices, specifically testing the fundamental operations of matrix arithmetic.
||KEY:B

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