We are given that,

Order of matrix A = 3 × 4

Order of matrix B = 4 × 3

We need to find the order of the matrix of AB.

We know that,

For matrices X and Y such that,

Order of X = m × n

Order of Y = r × s

In order to multiply the two matrices X and Y, the number of columns in X must be equal to the number of rows in Y. That is,

n = r

And order of the resulting matrix, XY is given as

Order of XY = m × s

Provided n = r.

So, we know

Order of A = 3 × 4

Here,

Number of rows = 3

Number of columns = 4

Order of B = 4 × 3

Here,

Number of rows = 4

Number of columns = 3

Note that,

Number of columns in A = Number of rows in B = 4

So,

Order of the resulting matrix, AB is given as

Order of AB = 3 × 3

Thus, order of AB = 3 × 3