How would I find a 2x2 matrix to multiply another 2x2 matrix by to get zero if that matrix is not the zero matrix? Specifically I have
[1 2]
[3 4] times B = 0
Let the unknown matrix be
We want:
Thus we need the solution to the systems:
..............(1)
..............(2)
and
....................(1)
...................(2)
Can you take it from here?
(That's the systematic way to do it, but really, as with numbers, multiplying any number by zero gives zero, so too with matrices: any matrix times the zero matrix gives the zero matrix, you will find that the solution to the above systems is a = b = c = d = 0)