A= 4 −2
−1 3

1. find the inverse of a. show your work, and confirm your answer.
2. explain why the matrix 3
4 2
has no inverse

1.

2.

Step-by-step explanation:

We have the matrix:

It's a 2×2 matrix (This means that the matrix has two rows and two columns).

1. We have to find the inverse of A.

For a 2×2 matrix the inverse is:

If you have

And,

is the determinant of the matrix, the determinant has to be different from zero.

If then the matrix doesn't have inverse.

Then,

First we are going to calculate the determinant:

The determinant is different from zero, then the matrix has inverse.

Then the inverse of A is:

2. We have the matrix,

We have to calculate the determinant:

We said that a matrix can have an inverse only if its determinant is nonzero.

In this case then, the matrix B doesn't have inverse.