Is this statement true or false

if false a counterexample is needed

if true then an explanation

The productAB of two square matrices can only have an inverse if A and B

both have inverses.

- Feb 17th 2011, 06:43 AMmaximus101Statement about the product AB of two square matrices, true or false?Is this statement true or false

if false a counterexample is needed

if true then an explanation

The productAB of two square matrices can only have an inverse if A and B

both have inverses.

- Feb 17th 2011, 06:53 AMAckbeet
What ideas have you had so far?

- Feb 17th 2011, 08:14 AMTinyboss
A matrix specifies a linear transformation. If a matrix is (or is not) invertible, what does that tell you about the rank of the associated linear transformation? Multiplying the matrices corresponds to composing the transformations.

- Feb 18th 2011, 03:38 AMHallsofIvy
Another way of thinking about it- a matrix is invertible if and only if its determinant is non-zero. And det(AB)= det(A)det(B).