show that there is no turing machine(TM) which given our encoding of any TM M as input will eventually halt outputting 1 if M started on a blank tape ever prints A, and outputting 0 if M started on a blank tape never prints the symbol A.

Is the best way to answer this question using a flow diagram eg

start( input encoding of M and encoding of tape T)

then ( construct encoding of M', which given our blank tape, first which converts it to T then runs M on it) then (would M' started on a BT ever halt)

ythen out put 1 or 0 if no.. but since this is the Blank tape halting problem, it leads us to a contradiction.. hence no TM exist ??