How do I find if a matrix has an inverse? I know how to tell if two matrices are inverses, but not how to find if one has an inverse.

Question

rational · Answer

you finished with probability !

rational · Answer

if a matrix has an inverse, then  the determinant is not 0 

if the determinant is not 0, then the matrix has an inverse

bloomlocke367 · Answer

Yep! and matrices are kind of a review for me, but I don't have a calculator, and I don't know how to do this without a calculator.

rational · Answer

$$\text{determinant is not zero} \iff     \text{invertible}$$

rational · Answer

whats teh exact complete question

bloomlocke367 · Answer

does the matrix, A have an inverse? If so, what is $A^{-1}$?$$\left[\begin{matrix}-7 & -25 \ 2 & 7\end{matrix}\right]$$

rational · Answer

do you know how to find the determinant ?

rational · Answer

bloomlocke367 · Answer

yes. ad-cb. where, $$\left[\begin{matrix}a & b \ c & d\end{matrix}\right]$$

rational · Answer

Yes start by finding the determinant

bloomlocke367 · Answer

1

rational · Answer

$1 \ne 0$
so the inverse exists, go ahead and find it

bloomlocke367 · Answer

how?

rational · Answer

bloomlocke367 · Answer

so it's just $$\left[\begin{matrix}7 & 25 \ -2 & -7\end{matrix}\right]$$

bloomlocke367 · Answer

right?

rational · Answer

Yep! since the determinant is 1, dividing by 1 wont change the matrix