Question

how i can justify that when determinant is nonzero matrix is invertible

Answer 1

What??? the question was 5 months ago??? still need help??

Answer 2

mm.. just for curiosity

Answer 3

1) the matrix must be a square matrix to consider whether its determinant =0 or not
2) if it is not 0, then it is invertible
3) the invertible matrix is defined by formula \(\dfrac{1}{determinant~~of~~original~~one}*\text{cofactor matrix}\)
Hence if determinant of the original one =0, the invertible matrix is undefined.