What is the order of \(\begin{bmatrix} 4 & 4 & 1 \end{bmatrix}\begin{bmatrix} 3&2 &5\\ 9& 7 & 4\\ 6& 4 & 1 \end{bmatrix} \)?

Concept:

• Order of a matrix is determined by the number of rows and columns the matrix consists.
• To multiply an m × n matrix by an n × p matrix, the n must be the same, and the result is an m × p matrix.

Calculation:

We have to find the order of \(\begin{bmatrix} 4 & 4 & 1 \end{bmatrix}\begin{bmatrix} 3&2 &5\\ 9& 7 & 4\\ 6& 4 & 1 \end{bmatrix} \)

Let \(​​\begin{bmatrix} 4 & 4 & 1 \end{bmatrix}\begin{bmatrix} 3&2 &5\\ 9& 7 & 4\\ 6& 4 & 1 \end{bmatrix} = {\rm{AB}}\)

Order of matrix A is (1 × 3)

Order of matrix B is (3 × 3)

Now, Order of A (1 × 3) B (3 × 3) is (1 × 3)

∴ Order of AB =(1 × 3)

So, Option 2nd is the correct answer.