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Question

If A and B are two matrices such that A has all identical rows and AB is defined. Then AB has

A
no identical rows
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B
identical rows
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C
all of its zeros
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D
cannot be determined
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Solution

The correct option is C identical rows
A=⎢ ⎢ ⎢ ⎢ ⎢ ⎢abc....iabc...i..........abc....i⎥ ⎥ ⎥ ⎥ ⎥ ⎥m×nB=⎢ ⎢ ⎢ ⎢ ⎢ ⎢kl....xwv...y........qr....s⎥ ⎥ ⎥ ⎥ ⎥ ⎥n×p
AB=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ak+bw+...+iqal+bv+..+ir.....ax+by+...+isak+bw+...+iqal+bv+..+ir.......ax+by+...+is........ak+bw+...+iqal+bv+..+ir........ax+by+...+is⎥ ⎥ ⎥ ⎥ ⎥ ⎥m×p
Hence, the rows are identical

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