Question

Explain why any patternPin a matrixA, other than the diagonal pattern, contains at least one entry below the diagonal and at least one entry above the diagonal.

Short answer

Therefore, the any pattern Pin a matrix was explained.

Step-by-step solution

Matrix Definition. 

Matrix is a set of numbersarranged in rows and columns soas to form a rectangulararray.

The numbers are called the elements, or entries, of the matrix.

If there are rows and columns, the matrix is said to be an “ mby n” matrix, written “$m\times n$.”

Explanations. 

The diagonal pattern in an$n\times n$matrix corresponds to the identity permutation. If we take any permutation

$p=\left(\begin{array}{ccc}1& ...& n\\ p_1& ...& p_n\end{array}\right)$

other than the identity, then there exists at least one number $i\in \left\{1,...,n\right\}$such that$p_i>i$ and at least one $i\in \left\{1,....,n\right\}$such that $p_j<j$. The pattern of that corresponds to this permutation will include $a_{i,pi}$, which is above the main diagonal, as well as $a_{j,p_j}$, which is below the main diagonal.