Consider the matrix:

$$\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right)$$

There are two ways to enter a matrix in your calculator.

1. First Way: If you just want to use the matrix for one computation, press and select Matrix & Vector > Create > Matrix. Choose the proper dimensions (here, Number of rows = 2 and Number of columns = 2), and press . You can then fill the matrix as follows:

   

2. Second Way: If you want to store the matrix in the calculator, do the same process. Then, press and . Enter the name of the matrix, here it is A.

   

Consider the matrix:

$$A=\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right)$$

Once you have entered it ( see above), you can display it in the main screen by entering A and pressing .

The matrix is displayed.

Suppose you have two matrices:

$$A=\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right),B=\left(\begin{array}{cc}5& 6\\ 7& 8\end{array}\right)$$

We can perform the following operations:

1. Addition: Enter A + B and press .

   

   The result is: $$A+B=\left(\begin{array}{cc}6& 8\\ 10& 12\end{array}\right)$$

2. Subtraction: Enter A - B and press . The result is: $$A-B=\left(\begin{array}{cc}-4& -4\\ -4& -4\end{array}\right)$$
3. Multiplication: Enter A x B and press . The result is: $$A\ast B=\left(\begin{array}{cc}19& 22\\ 43& 50\end{array}\right)$$

Note: To perform matrix operations, ensure that the matrices are of compatible dimensions.

Identity and zero matrices are fundamental in matrix operations. Here’s how to create them:

1. Create an Identity Matrix:
   1. Press and select Matrix & Vector > Create > Identity.
   2. Enter the size of the matrix (e.g., 3 for a 3x3 identity matrix) and press .

   The result should be:

   $$I=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)$$

2. Create a Zero Matrix:
   1. Press and select Matrix & Vector > Create > Zero Matrix.
   2. Enter the dimensions of the matrix (e.g., 3 rows and 2 columns for a 3x2 zero matrix) and press .

   The result should be:

   $$Z=\left(\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\end{array}\right)$$

Identity and zero matrices are useful for checking properties such as inverses and simplifying operations.

Consider the matrix:

$$A=\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right)$$

To compute the determinant:

1. Enter the matrix ( see above)
2. Press and select Matrix & Vector > Determinant.
3. Enter A (or the matrix directly) and press .

   

   The result should be $\text{det}(A)=3$.

Consider the matrix:

$$A=\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right)$$

To compute the inverse:

1. Enter A^-1 (using the power key ).
2. Press . The following result should be displayed:

   

Note: The matrix must be square and have a non-zero determinant to have an inverse.