We are given that,

We need to find the order of the matrix A.

Let the matrices be,

Let us find the order of X.

Number of rows of matrix X = 1

Number of columns of matrix X = 3

So, order of matrix X = 1 × 3 …(i)

Now, let us find the order of Y.

Number of rows of matrix Y = 3

Number of columns of matrix Y = 3

So, order of matrix Y = 3 × 3 …(ii)

From (i) and (ii),

Order of resulting XY = 1 × 3 [∵, Number of columns of X = Number of rows of Y] …(iii)

Let us find the order of Z.

Number of rows of matrix Z = 3

Number of columns of matrix Z = 1

So, order of matrix Z = 3 × 1 …(iv)

Order of resulting XYZ = 1 × 1 [∵, Number of columns of XY = Number of rows of Z]

Thus, the order of matrix A = 1 × 1