math
posted by katy on .
Why is (AB)^1 = B^1A^1 in matrices, and not (AB)^1 = A^1B^1

let A be an m by n matrix and B be a n by p matrix. Then A*B is defined. Also, A^1 is an n by m matrix, and B^1 is an p by n matrix. So B^1 * A^1 is also defined, but A^1 * B^1 may not be.
Or, in other words, the commutative property of scalar multiplication does not apply to matrices.