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If A is a $2 \times 3$ matrix and $\mathrm{AB}$ is a $2 \times 5$ matrix, then B must be a
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$3 \times 5$ matrix
A is $2 \times 3$ matrix
$\mathrm{AB}$ is $2 \times 5$ matrix
Let ' $\mathrm{B}$ ' bem $\times \mathrm{n}$ matrix
$[\mathrm{A}]_{2 \times 3}[\mathrm{~B}]_{\mathrm{m} \times \mathrm{n}}=[\mathrm{AB}]_{2 \times 5}$
number of columns of $\mathrm{A}=$ number of rows of $\mathrm{B}$. $\therefore m=3$
we can observe that $\mathrm{n}=5$ from the product. So, $\mathrm{B}$ is $3 \times 5$ matrix.
$\mathrm{AB}$ is $2 \times 5$ matrix
Let ' $\mathrm{B}$ ' bem $\times \mathrm{n}$ matrix
$[\mathrm{A}]_{2 \times 3}[\mathrm{~B}]_{\mathrm{m} \times \mathrm{n}}=[\mathrm{AB}]_{2 \times 5}$
number of columns of $\mathrm{A}=$ number of rows of $\mathrm{B}$. $\therefore m=3$
we can observe that $\mathrm{n}=5$ from the product. So, $\mathrm{B}$ is $3 \times 5$ matrix.
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