Samyak Jain
Last Activity: 5 Years ago
Matrix X has (a + b) rows and (a + 2) columns and matrix Y has (b + 1) rows and (a + 3) columns.

XY exists, number of columns of X = number of rows of Y i.e.
a + 2 = b +1 or a = b – 1.

YX exists, number of columns of Y = number of rows of X i.e.
a + 3 = a + b or b = 3.

a = 3 – 1 or
a = 2.
This shows that X has 5 rows and 4 columns; has order 5x4. Y has 4 rows and 5 columns; has order 4x5.
We know that number of rows and columns of AB equals the number of rows of X and the number of columns of Y respectively if AB exists.

XY has order 5x5 and YX has order 4x4. XY and YX are square matrices and hence are of the same type.
But they aren’t equal as their orders are different.