Question

If A and B are two matrices of orders a × 3 and 3 × b respectively such that AB exists and is of order 2 × 4. Then, (a, b) = ___________.

Answer 1

Let $X={\left[x_{ij}\right]}_{m\times n}$ and $Y={\left[y_{ij}\right]}_{p\times q}$ be two matrices of order m × n and p × q. The multiplication of matrices X and Y is defined if number of columns of X is same as the number of rows of Y i.e. n = p. Also, XY is a matrix of order m × q.


A and B are two matrices of orders a × 3 and 3 × b, respectively.

So, AB is a matrix of order a × b.

It is given that, AB exists and its order 2 × 4.

∴ a = 2 and b = 4

Thus, the ordered pair (a, b) is (2, 4).

If A and B are two matrices of orders a × 3 and 3 × b respectively such that AB exists and is of order 2 × 4. Then, (a, b) = ___(2, 4)___.