Given: Order of A is 4 × 3, the order of B is 4 × 5 and the order of C is 7 × 3 The transpose of the matrix obtained by interchanging the rows and columns of the original matrix. So, order of AT is 3 × 4 and order of CT is 3 × 7 Now, ATB = {3 × 4} {4 × 5} = 3 × 5 ⇒ Order of ATB is 3 × 5 Hence order of (ATB)T is 5 × 3 Now order of (ATB)TCT= {5 × 3} {3 × 7} = 5 × 7 ∴ Order of (ATB)TCT is 5 × 7