Question

a matrix X has a+b rows and a+2 columns while the matrix Y has b+1 rows and a+3 columns. both matrices XY and YX exist. find a and b. can you say XY and YX sre of same type? are they equal?

Answer 1

[X]
a+b*a+3;
[Y]
b+1*a+3;
so,
a+2=b+1 ...1
a+b=a+3
a is cut so,
b=3,
now,
put b=3 in (1)
a+2=3+1
a=4-2
a=2
a=2 and b=3.
XX and YX are not of the same type .they are unequal.

Answer 2

Did you meant
[X]
a+b*a+2;

instead of
[X]
a+b*a+3;