If A is 3 × 4 matrix and B is a matrix such that A'B and BA' are both defined.


If $A$ is $3 \times 4$ matrix and $B$ is a matrix such that $A^{\prime} B$ and $B A^{\prime}$ are both defined. Then, $B$ is of the type

(a) $3 \times 4$

(b) $3 \times 3$

(c) $4 \times 4$

(d) $4 \times 3$


(a) $3 \times 4$

The order of $A$ is $3 \times 4$. So, the order of $A$ ' is $4 \times 3$.

Now, both A'B and BA'">A'B and BA'A'B and BA' are defined. So, the number of columns in A' should be equal to the number of rows in B for A'B.
Also, the number of columns in B should be equal to number of rows in A' for BA'.

Hence, the order of matrix B is 3 ×">×× 4.

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