Not all numbers have an inverse

Matrix inverse:
If A is an \(m\times m\) matrix, and if it has an inverse,

\(I\)是单位矩阵，同时\(A\)是square matrix 即方阵（线性代数领域）。

Matrices that don't have an inverse are "singular or degenerate". (奇异矩阵或退化矩阵)

Matrix Transpose

Example:
\(A=\begin{bmatrix} 1&2&0\\ 3&5&9\\ \end{bmatrix}\)??\(A^T=\begin{bmatrix} 1&3\\ 2&5\\ 0&9\\ \end{bmatrix}\)

Let A be an \(m\times n\) matrix, and let \(B=A^T\).
Then \(B\) is an \(n\times m\) matrix, and