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

no identical rows

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identical rows

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all of its zeros

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cannot be determined

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Solution

The correct option is C identical rows
$A = {⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} a & b & c & . . . . & i a & b & c & . . . & i . & . & . & . & . . & . & . & . & . a & b & c & . . . . & i \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦}_{m \times n} B = {⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} k & l & . . . . & x w & v & . . . & y . & . & . & . . & . & . & . q & r & . . . . & s \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦}_{n \times p}$
$A B = {⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} a k + b w + . . . + i q & a l + b v + . . + i r & . . . . . & a x + b y + . . . + i s a k + b w + . . . + i q & a l + b v + . . + i r & . . . . . . . & a x + b y + . . . + i s . & . & . & . . & . & . & . a k + b w + . . . + i q & a l + b v + . . + i r & . . . . . . . . & a x + b y + . . . + i s \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦}_{m \times p}$
Hence, the rows are identical

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Similar questions

If $A$ and $B$ are two matrices such that $A$ has identical rows and $A B$ is defined, then $A B$ has

A

B

A + B

A B

A

B

A B

A + B

A

B

B^{2}

A

B

A B = 0

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