# Determine whether the statement is true or false and explain a) There exist two 1*1 mattrices A and B such AB≠BA b)There exist two 2*2 matrices A and B such that AB≠BA c)There exist two nonzero 2*2 matrices A and B such that AB is the 2*2 zero matrix d)There exist two nonzero 1*1 matrices A and A such that AB is the 2*2 zero matrix

1
by mrambabu1600

2015-03-15T10:24:47+05:30

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A)FALSE
Let A=[x] and B=[y] be any two 1*1 matrices.
AB = [x]*[y] = [xy]
BA = [y]*[x] = [xy]
So AB=BA.

b)TRUE.
There are many such matrices. One example is:

c)TRUE
You can find many such matrices.

d)FALSE.
Product of two 1*1 matrix is always a 1*1 matrix only. It can't be a 2*2 matrix.
If both A and B are non-zero, then AB can't be even a 1*1 zero matrix.