Question

Consider two square matrices a and b with dimension m x m. Ab = ba

Answer 1

Answer:

A*b=b*a

if

A=a=b= $\left[\begin{array}{cc}1&0\\0&1\\\end{array}\right]$

Step-by-step explanation:

To Find:

A*b=b*a

Solution:

if A=b=a=$\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

then

A*b=$\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

Similarly

b*a=$\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

which shows that:

A*b=b*a   Proved

Answer 2

a*b =  [ 1 0 ]  = b*a    

         [ 0 1 ]            

ab = ba

GIVEN: Two Square matrices a and b of dimensions m*m
TO PROVE: ab = ba
SOLUTION:

As we are given,

We have two square matrices a and b with the dimensions as m*m.

Let us assume the matrices a = b = [ 1 0 ]    

                                                          [ 0 1 ]

With dimensions as 2*2

Therefore,

Matrix a =  [ 1 0 ]    

                 [ 0 1 ]

Similarly,

Matrix b = [ 1 0 ]    

                 [ 0 1 ]

Now,

We find a*b,

a*b =  [ 1 0 ]    

          [ 0 1 ]                               ------Equation 1

Also,

For b*a,

b*a = [ 1 0 ]    

         [ 0 1 ]                               ------Equation 2

Now,

From equation 1 and2

We get,

a*b =  [ 1 0 ]  = b*a = [ 1 0 ]    

         [ 0 1 ]               [ 0 1 ]  

Therefore we get,

a*b =  [ 1 0 ]  = b*a    

         [ 0 1 ]            

a*b = b*a

Hence proved.

#SPJ2