True False Problem

Enter T or F depending on whether the statement is true or false. $($You must enter T or F $--$ True and False will not work.$)$

If A and $B$ are both square matrices such that $AB$ equals $BA$ equals the identity matrix, then $B$ is the inverse matrix of $A.$

If $A$ is a square matrix, then there exists a matrix $B$ such that $AB$ equals the identity matrix.