Question

Suppose A is an n x n matrix. How can you tell if A has an inverse?

Answer 1

An n x n matrix has an inverse if and only if its determinant is nonzero. To check if a matrix has an inverse, calculate its determinant. If the determinant is nonzero, then the matrix has an inverse. If the determinant is zero, then the matrix does not have an inverse.

Step-by-step explanation:

An n x n matrix has an inverse if and only if its determinant is nonzero. To check if a matrix has an inverse, calculate its determinant. If the determinant is nonzero, then the matrix has an inverse. If the determinant is zero, then the matrix does not have an inverse.

For example, let's consider a 2 x 2 matrix:
A = ( a b )
( c d )

The determinant of A is calculated as: det(A) = ad - bc.

If det(A) ≠ 0, then A has an inverse. If det(A) = 0, then A does not have an inverse.