What is a singular matrix?

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Solution

Singular matrix: A square matrix is singular if and only if the value of its determinant is zero.
The inverse of a singular matrix does not exist.
Example: $A = [\begin{matrix} 2 & 1 \\ 6 & 3 \end{matrix}]$
The determinant of the matrix is,
$|A| = 2 \cdot 3 - 6 \cdot 1$
$\Rightarrow$ $|A| = 6 - 6$
$\Rightarrow$ $|A| = 0$
Hence, the matrix $A$ is a singular matrix.

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Q. If A is a singular matrix, then A (adj A) = ____________________.

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(a) null matrix
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(c) unit-matrix
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What is a singular matrix?

Singular matrix: A square matrix is singular if and only if the value of its determinant is zero.The inverse of a singular matrix does not exist.Example: A=2163The determinant of the matrix is, A=2·3-6·1⇒ A=6-6⇒ A=0Hence, the matrix A is a singular matrix.