Let A, B, C, D be matrices such that:(adsbygoogle = window.adsbygoogle || []).push({});

AB + CD = 0

and

B is invertible. Moreover, consider the dimension restrictions:

A(m x n), B(n x n), C(m x m), D(m x n)

If C is a square matrix, is there a way to show that it is also invertible with only the above conditions?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Determining invertibility of a matrix

**Physics Forums | Science Articles, Homework Help, Discussion**