Any given square matrix A is said to be Invertible if its inverse exists. In other words, we can say that square matrix A is said to be Invertible if there exists another square matrix B such that where I is an identity matrix of same order as of A and B.
How do we get to know that given matrix is Invertible?
If, determinant of given square matrix A is non-zero then it means Inverse of matrix exists. So, if we have any matrix having determinant equal to 0 then it is non-invertible.
This condition comes from the fact that (1)
where is Inverse of Matrix A,
Adj(A) is adjoint of matrix A,
and det(A) is determinant of matrix A.
From (1), we can see that if det(A)=0 then would not exist.