If <img wid

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