Matrix X has a + b rows and a + 2 columns
Matrix Y has b + 1 rows and a + 3 columns.
Since XY is defined
∴ number of columns of X = number of rows of Y
∴ a + 2 = b + 1
∴ a – b + 1 = 0    ...(1)
Again YX is defined
∴number of columns of Y = number of rows of X
∴a + 3 = a + b ⇒ b = 3
Putting b = 3 in (1), we get,
a –3 + l = 0 ⇒ a = 2
∴ we have a = 2, b = 3
∴ X is of type 5 x 4 and Y is of type 4 x 5.
∴ XY is of type 5 x 5 and YX is of type 4 x 4.
So XY and YX are not of the same type and so XY ≠ YX,