Prove that if is a matrix with and is a matrix satisfying

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Prove that if

A

is a

2\times 2

matrix with

\det A\neq 0

and

B

is a

2\times 2

matrix satisfying

AB=O_{2\times 2}

, then

B=O_{2\times 2}