Question

If P and Q are two matrices of orders 3 × n and n × p respectively then the order of the matrix PQ is ___________.

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.


It is given that, P and Q are two matrices of orders 3 × n and n × p, respectively.

∴ Order of the matrix PQ = 3 × p

If P and Q are two matrices of orders 3 × n and n × p respectively then the order of the matrix PQ is ___3 × p___.