**Question:**

If $P$ and $Q$ are two matrices of orders $3 \times n$ and $n \times p$ respectively then the order of the matrix $P Q$ is________

**Solution:**

Let $X=\left[x_{i j}\right]_{m \times n}$ and $Y=\left[y_{i j}\right]_{p \times q}$ be two matrices of order $m \times n$ and $p \times q$. 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, $X Y$ is a matrix of order $m \times q$.

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

$\therefore$ Order of the matrix $P Q=3 \times p$

If $P$ and $Q$ are two matrices of orders $3 \times n$ and $n \times p$ respectively then the order of the matrix $P Q$ is $3 \times p$