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math125-lecture 3.2

# math125-lecture 3.2 - Sec 3.2 Saturday 11:16 PM A matrix B...

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A matrix B is the multiplicative inverse of the matrix A if A B = I and B A = I Notation: The multiplicative inverse of A is denoted A -1 For a real number a , if b satisfies ab = 1 = ba , then b = = a -1 1 a Sec 3.2 Saturday, February 06, 2010 11:16 PM Section3dot2 Page 1

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A matrix B is the multiplicative inverse of the matrix A if A B = I and B A = I Notation: The multiplicative inverse of A is denoted A -1 REMARKS: 1. If there is an inverse, there is just one 2. Only square matrices have inverses (why? check dimensions !) 3. Not every square matrix has an inverse For a real number a , if b satisfies ab = 1 = ba , then b = = a -1 1 a 3.2.1 Saturday, February 06, 2010 11:16 PM Section3dot2 Page 2