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

Answers

The Brainliest Answer!
2015-03-15T10:24:47+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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:
  A=\left[\begin{array}{cc}1&2\\4&5\end{array}\right];\ B=\left[\begin{array}{cc}0&0\\0&1\end{array}\right] \\ \\AB= \left[\begin{array}{cc}0&2\\0&5\end{array}\right] ;\ BA= \left[\begin{array}{cc}0&0\\4&5\end{array}\right] \\ \\Thus\ AB \neq BA

c)TRUE
You can find many such matrices.
  A=\left[\begin{array}{cc}3&6\\2&4\end{array}\right];\ B=\left[\begin{array}{cc}2&-8\\-1&4\end{array}\right]\\You\ can\ check\ that\ AB=0.

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. 
2 5 2