Determine the product of two matrices and calculate the inverse of the 2 X 2 matrix.

• Determine the product of two matrices
• Calculate the inverse of the 2 X 2 matrix
• Demonstrate that when [A][B] = [C], [A] = [C][B]^-1

• Encryption key
• Inverse matrix

In this lesson a secret word, which is represented by a 2 X 2 matrix, has been coded using an encryption key. Students will be given the encryption key, along with the matrix that represents the coded word. By calculating the inverse of the encryption key, students will determine the secret word. Students will then create their own encryption key and secret words, exchange them with their partners, and decode them by calculating the inverse of their encryption keys. As a result, students will make conjectures about the relationships between matrices and their inverses.

NOTE: A teacher .TNS document has also been included with this activity which performs the required matrix multiplication and inverse steps as well.