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**Identity and Inverse Matrices**

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The Identity Matrix The identity matrix [I] for multiplication is a square matrix with a 1 for every element of the principal diagonal (top left to bottom right) and a 0 in all other positions. Example: 3x3 Identity Matrix

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Identity Matrix A I = A A =

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Inverse Matrix The product of a matrix and its inverse is the identity matrix. A-1 is the notation to designate the inverse of a matrix. A A-1 = I

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**Since XY≠I, they are not inverses!**

Verify Inverse Matrices: Determine whether the pair of matrices are inverses. Since XY≠I, they are not inverses!

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**Find the inverse of the matrix.**

Step 1: Find the determinant. Step 2: Multiply by

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**Find the inverse of the matrix.**

Step 1: Find the determinant. Step 2: Change the matrix: Step 3: Multiply by

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**Find the inverse of each matrix.**

Step 1: Find the determinant of the matrix. Since the determinant equals 0, R-1 does not exist.

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