1. A square matrix is a matrix with the same number of columns as rows.

2. Determinant of a 3 x 3 Matrix
The determinant of a 3 x 3 matrix
a1 b1 c1
a2 b2 c2
a3 b3 c3
is (a1b2c3 +
b1c2a3
+ c1a2b3)
- (a3b2c1 +
b1a2c3
+ a1b3c2)

3. Evaluating the Determinant of a 3 x 3 Matrix
Evaluate each determinant.
0 4 1 18 19
0 2 3
0 0 0 27

4. Finding the Determinant using Graphing Calculator
Steps:
Input the given matrix A into your graphing calculator.
Use the matrix submenus to evaluate the determinant of A
2nd
matrix
MATH
1:det(
2nd
NAMES
matrix A
ENTER

5. Finding the Inverse using Graphing Calculator
Steps:
Input the given matrix A into your graphing calculator.
Use the matrix submenus to find the inverse of A.
2nd
matrix
NAMES
matrix A
X-1

6. Finding the Inverse of a 3 x 3 Matrix
Find the inverse of each of the following matrices .
0 4 1
46/ / /19
/ /19
-12/ / /19
-1/9 4/9 19/9
1/9 1/18 8/9
1/9 1/18 -1/9

7. Solving a Matrix Equation
Solve the equation
0 0 2
X = 6
-11 8
AX = B
X = A-1B
X = 1 -2 3

8. Solve the given equations.1. 2.
0 0 2
X = -6 19
X = 9 -5
X = 5 2
X = 3 -2 2