KCET · Maths · Matrices
If \( \mathrm{A} \) is a matrix of order \( \mathrm{m} \times \mathrm{n} \) and \( \mathrm{B} \) is a matrix such that \( \mathrm{AB}^{\prime} \) and \( \mathrm{B}^{\prime} \mathrm{A} \) are both defined, the
order of the matrix \( B \) is
- A \( \mathrm{m} \times \mathrm{m} \)
- B \( n \times n \)
- C n \( \times m \)
- D \( \mathrm{m} \times \mathrm{n} \)
Answer & Solution
Correct Answer
(D) \( \mathrm{m} \times \mathrm{n} \)
Step-by-step Solution
Detailed explanation
Given that, matrix \(\mathrm{A}\) is \(\mathrm{m} \times \mathrm{n}\)
Let matrix \(\mathrm{B}\) is \(x \times y\).
So, \(\mathrm{AB}^{\prime}\) is defined then, \(\mathrm{n}=\mathrm{y}\)
Similarly, \(\mathrm{B}\) 'A is defined then, \(\mathrm{x}=\mathrm{m}\)
Therefore, order of matrix \(\mathrm{B}\) is \(\mathrm{m} \times \mathrm{n}\).
Let matrix \(\mathrm{B}\) is \(x \times y\).
So, \(\mathrm{AB}^{\prime}\) is defined then, \(\mathrm{n}=\mathrm{y}\)
Similarly, \(\mathrm{B}\) 'A is defined then, \(\mathrm{x}=\mathrm{m}\)
Therefore, order of matrix \(\mathrm{B}\) is \(\mathrm{m} \times \mathrm{n}\).
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