1) Perform a Gaussian elimination. Then if you end up with a matrix with all zeros in a row, your matrix is not invertible. 2) Compute the determinant of your matrix, using the fact that a matrix is invertible if its determinant is non-zero.
Is a matrix invertible if the determinant is 0?
If the determinant of a square n×n matrix A is zero, then A is not invertible. This is a crucial test for determining whether a square matrix is invertible, i.e. whether the matrix has an inverse.
What is the theorem of invertible matrices?
The invertible matrix theorem is a linear algebra theorem that provides a list of equivalent conditions for a square n × n matrix A to have an inverse. … A is a row corresponding to the n × n identity matrix I_n. A has n pivot positions. The equation Ax=0 has only the trivial solution x=0.