If A is a 2 × 3 matrix and A B is a 2 × 5 matrix, then B must be a

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