Suppose P and Q are two different matrices of order 3 × n and n × p , thenthe order of the matrix P × Q is?

Break Down the Problem

1. Identify the order of matrix $P$.
2. Identify the order of matrix $Q$.
3. Determine the resulting order when multiplying these two matrices.

Relevant Concepts

1. The order of a matrix is defined by the number of rows and columns it has.
2. When multiplying two matrices, if matrix $A$ is of order $m \times n$ and matrix $B$ is of order $n \times p$, the resulting matrix $AB$ will be of order $m \times p$.

Analysis and Detail

1. Matrix $P$ has the order $3 \times n$.
2. Matrix $Q$ has the order $n \times p$.
3. Therefore, when multiplying $P$ and $Q$: $P \times Q = \text{Order of } (3 \times n) \times (n \times p) = 3 \times p$

Verify and Summarize

• The multiplication is valid since the number of columns in $P$ (which is $n$) matches the number of rows in $Q$ (also $n$).
• The resulting matrix from $P \times Q$ will indeed have the order $3 \times p$.

Final Answer

The order of the matrix $P \times Q$ is $3 \times p$.