* If has an inverse (and it might not!), then , where is the identity matrix.
* The identity matrix doesn't change any matrix that it multiplies. So, for instance, and .
* Matrix multiplication is not commutative; that is to say, the matrix product is not in general equal to the product .
* When multiplying two matrices, and , say, the matrices must have 'compatible' dimensions. That is, in order to form the product , the number of columns in must be the same as the number of rows in . So if is a matrix, must be a matrix, for some values of , and .
So, to answer your questions:
1 True, because , and .
2 If you have to say True or False, then you'd say False. But in fact it's meaningless, because is impossible to form unless - the dimensions are incompatible. If you had to write a correct version then you'd say .
3 The same applies here: neither nor are possible products unless . A correct statement would be , which is just the same as number 2 really.