Show that the matrices a = [1 2 -1 4] and b = [2/3 -1/3 1/6 1/6] are multiplicative inverses in m_2, 2.

Proof:

Let's Multiply them!

If you don't remember how to multiply matrices, don't worry. In order to get AB we focus on the rows of A, and the columns of B.

The first row of A is [1 2] and the first column of B is [2/3 1/6], if we do de dot multiplication we get 1(2/3) + 2(1/6) = 2/3 + 1/3 = 1.The first row of A is [1 2] and the second column of B is [-1/3 1/6]. Here we get 1(-1/3) + 2(1/6) = -1/3 +  1/3 = 0.The second row of A is [-1 4] and the first column of B is  [2/3 1/6]. Here we get -1(2/3) + 4(1/6) = -2/3 + 2/3 = 0.The second row of A is [-1 4] and the second column of B is [-1/3 1/6]. Here we get -1(-1/3) + 4(1/6) = 1/3 + 2/3 = 1.

Then  

We also have to see what happens with .

With this, we can conclude that

where is the identity matrix. An by definition, that means that and   are multiplicative inverses.

The answer is : 63explanation 60 times 0.05360+363