Let A and B be matrices of orders 3 × 2 and 2 × 4 respectively. Write the order of matrix AB.

We are given that,

Order of matrix A = 3 × 2

Order of matrix B = 2 × 4

We need to find the order of matrix AB.

We know that,

Matrix A × Matrix B = Matrix AB

If order of matrix A is (m × n) and order of matrix B is (r × s), then matrices A and B can be multiplied if and only if n = r.

That is,

Number of columns in A = Number of rows in B

Also, the order of resulting matrix AB comes out to be m × s.

Applying it,

Number of columns in A = 2

Number of rows in B = 2

This means,

Matrices A and B can be multiplied, and its order will be given as:

Order of matrix AB = 3 × 4

Thus, order of matrix AB = 3 × 4