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 $YX$ are of the same type? Are they equal?

Give an example of matrices $A$ and $B$ such that $AB\ne BA$.

Give an example of matrices $A$ and $B$ such that $AB=O$ but $BA\ne O$.

If $A$ and $B$are square matrices of the same order, explain, why in general $(A-B{)}^2\ne A^2- 2AB+B^2$?

If $A$ and $B$ are square matrices of the same order, explain, why in general

 $(A+B) (A-B) \ne A^2-B^2$