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(AB) (B-1 A-1) = A (BB-1) A-1 , by associativity.

= A I A-1 = AA-1 = I

Properties of the Matrix Inverse

The answer to the question shows that:

(AB)-1 = B-1 A-1

Notice that the order of the matrices has been reversed on the right of the "=" . Another sometimes useful property is:

(A-1)T = (AT)-1


What is the determinant of:

 1   3
-1   2

(If you have forgotten about determinants, or wish you had, don't worry. They won't be used much.)