Question:
Let $A$ be $3 \times 3$, $B$ be $3 \times 2$ and $C$ be $3 \times 1$. Which one of the following products is not defined? ________.
Let $A$ be $3 \times 3$, $B$ be $3 \times 2$ and $C$ be $3 \times 1$. Which one of the following products is not defined? ________.
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$(m \times n) \times (n \times p) \to m \times p$.
Updated On: Jun 26, 2026
- $C^{T}AB$
- $A^{T}AB$
- $(AB)^{T}C$
- $(AB)C$
- $B^{T}C$
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Product $XY$ is defined if the number of columns in $X$ equals the number of rows in $Y$.
Step 2: Meaning
Order of $A = 3 \times 3$, $B = 3 \times 2$, $C = 3 \times 1$.
Step 3: Analysis
Product $AB$: $(3 \times 3) \times (3 \times 2) \to$ defined, result is $3 \times 2$. Product $(AB)C$: $(3 \times 2) \times (3 \times 1)$. Number of columns (2) $\ne$ number of rows (3).
Step 4: Conclusion
$(AB)C$ is not defined. Final Answer: (D)
Product $XY$ is defined if the number of columns in $X$ equals the number of rows in $Y$.
Step 2: Meaning
Order of $A = 3 \times 3$, $B = 3 \times 2$, $C = 3 \times 1$.
Step 3: Analysis
Product $AB$: $(3 \times 3) \times (3 \times 2) \to$ defined, result is $3 \times 2$. Product $(AB)C$: $(3 \times 2) \times (3 \times 1)$. Number of columns (2) $\ne$ number of rows (3).
Step 4: Conclusion
$(AB)C$ is not defined. Final Answer: (D)
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