KCET · Maths · Matrices
If \(A\) and \(B\) are two matrices such that \(A B\) is an identity matrix and the order of matrix \(B\) is \(3 \times 4\), then the order of matrix A is
- A \(3 \times 4\)
- B \(3 \times 3\)
- C \(4 \times 3\)
- D \(4 \times 4\)
Answer & Solution
Correct Answer
(C) \(4 \times 3\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& \mathrm{AB}=\mathrm{I} \\
& \mathrm{~A}_{4 \times 3} \mathrm{~B}_{3 \times 4} \rightarrow \mathrm{I}_{4 \times 4}
\end{aligned}\)
\(\rightarrow\) The order of matrix A is \(4 \times 3\)
& \mathrm{AB}=\mathrm{I} \\
& \mathrm{~A}_{4 \times 3} \mathrm{~B}_{3 \times 4} \rightarrow \mathrm{I}_{4 \times 4}
\end{aligned}\)
\(\rightarrow\) The order of matrix A is \(4 \times 3\)
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