Answer :

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


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