Q58 / 160 · WBJEE 2011 · Mathematics

If \(\mathrm{A}\) and \(\mathrm{B}\) are two matrices such that \(\mathrm{A}+\mathrm{B}\) and \(\mathrm{AB}\) are both defined, then

  • A
    A and \(B\) can be any matrices
  • B
    A, B are square matrices not necessarily of the same order
  • Correct answer
    C
    A, B are square matrices of the same order
  • D
    Number of columns of \(A=\) number of rows of \(B\)

Solution

Hints : Addition is defined if order of \(A\) is equal to order of \(B\) A B \(\mathrm{nxm} \mathrm{nxm}\) is defined if \(\mathrm{m}=\mathrm{n}\) \(\Rightarrow A, B\) are square matrices of same order

Hence, the correct answer is option: 'C'.

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