Singular Matrix & Non Singular Matrix | Properties & Examples

Singular matrix is a square matrix whose determinant is zero. It is also known as non invertible matrix or degenerate matrix. A square matrix whose determinant is not zero is known as non singular matrix. It is also known as invertible matrix or non degenerate matrix.

A square matrix P is said to be singular matrix if |P| = 0. A square matrix Q is said to be non singular matrix if |Q| ≠ 0.

Singular matrix examples

The example of a singular matrix of order 3 (or matrix size is 3 x 3) is given below.

    \[A=\begin{bmatrix} 3 &8 &1 \\ -4& 1 &1 \\ -4&1 & 1 \end{bmatrix}\]

The example of a singular matrix of order 2 (or matrix size is 2 x 2) is given below.

    \[B=\begin{bmatrix} 1 &2 \\ 3& 6 \end{bmatrix}\]

Non Singular matrix examples

The example of non singular matrix of order 3 (or matrix size is 3 x 3) is given below.

    \[C=\begin{bmatrix} 1 &2 &3 \\ 4& 5 &6 \\ 7&8 & 9 \end{bmatrix}\]

The example of non singular matrix of order 2 (or matrix size is 2 x 2) is given below.

    \[D=\begin{bmatrix} 1 &0 \\ 0& 1 \end{bmatrix}\]

Singular matrix properties

1. The determinant of a singular matrix (P) is zero i.e. |P| = 0.

2. The inverse of a singular matrix does not exist. Hence it is also known as non-invertible matrix.

3. This matrix is always a square matrix because determinant is always calculated for a square matrix.

4. There is no multiplicative inverse exist for this matrix.

Non Singular matrix properties

1. The determinant of a non singular matrix (Q) is not zero i.e. |Q| ≠ 0.

2. The inverse of a non singular matrix does exist. Hence it is also known as invertible matrix.

3. Such matrix is always a square matrix because determinant is always calculated for a square matrix.

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