Square Matrix

A square matrix is a matrix with the same number of rows and columns. The dimension of a square matrix that has n rows and n columns is n* n. A_(n* n) = a_(11) & ⋯ & a_(1n) a_(21) & ⋯ & a_(2n) ... & ⋱ & ... a_(n1) & ⋯ & a_(nn) The entries a_(11), a_(22), a_(33), ..., a_(nn) in a square matrix together form its main diagonal. The following matrices have an equal number of rows and columns, making them square matrices. A_(2* 2) = 3 & - 4 5 & 2 & B_(3* 3) = 0 & - 1 & 3 6 & -2 & 17 - 12 & 9 & 7 Here, A has 2 rows and 2 columns, making it a 2* 2 matrix with four elements. Some important properties of square matrices can be listed as follows.

• If the main diagonal elements in a square matrix are ones and the rest of the elements are zeros, then the matrix is an identity matrix.
• The sum of all main diagonal elements in a square matrix is called the trace of the matrix.
• The determinant is only defined for square matrices
• Only square matrices can be invertible.
• If a square matrix's determinant is zero, then it is not invertible and is called singular.
• Any two square matrices of the same dimension can be added, subtracted, and multiplied.