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Unformatted text preview: In particular, the inverse of A is unique.
We have AB = In = BA and AC = In = CA. Therefore,
C = CIn = C (AB ) = (CA)B = In B = B If A is an invertible n × n matrix, we will denote its unique
inverse by A−1 .
Thus we have:
A−1 A = In = AA−1 . Outline Identity Matrices Inverse of a Matrix Inverses of 2 × 2 Matrices Theorem
, then A is invertible if and only if ad − bc = 0,
and in this case: If A = A−1 =
ad − bc d −b
a Outline Identity Matrices Inverse of a Matrix Inverses of Products Theorem
If A and B are invertible n × n matrices, then AB is invertible with
(AB )−1 = B −1 A−1
(AB )−1 = B −1 A−1 means that AB has inverse B −1 A−1 .
Check! Outline Identity Matrices Inverse of a Matrix Powers of Matrices Let r be a positive int...
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