# Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.
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cyhuddwyr9
Step 1
Consider a square matrix $A=\left[\begin{array}{ccc}0& 0& 0\\ 1& 2& 3\\ 4& 5& 6\end{array}\right]$ and $B=\left[\begin{array}{ccc}1& 4& 0\\ 2& 5& 0\\ 3& 6& 0\end{array}\right]$
Here, all the elements of first row of the matrix A and all the elements of third column of the matrix B are zero.
Step 2
Since, the determinant of a matrix is zero if all the elements of a row or column are zero.
Therefore, |A|=0 and |B|=0
If the determinant of a matrix is zero then the matrix is called singular matrix.
Hence, the square matrices A and B are singular.
Jeffrey Jordon