UPSC NDA Math Model Paper 10

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