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.
Example of Nilpotent Matrix: Video Tutorial
If, we have a given matrix A. We can perform some column and row operations on this matrix such that value of its determinant remains unchanged. If, we multiply particular row (column) of matrix A with a constant k and then add all the element of that row (column) to the corresponding elements of another row (column) then the value of determinant remains unchanged. This is an important property regarding matrices and determinants.