A matrix -B- is singular ifB is invertible-B- - 0-B- - 0-An inverse of B doesn-t exist-

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Singular and Non Singular Matrices

A matrix ‘B’ ...

Question

A matrix ‘B’ is singular if

B is invertible

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|B| = 0

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$| B | \neq 0$

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An inverse of B doesn’t exist

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Solution

The correct options are
B
|B| = 0

D
An inverse of B doesn’t exist

By definition a square matrix that doesn’t have a matrix inverse is called a singular matrix. For such a matrix the determinant will be 0 and for other matrices whose determinants are not equal to zero are called non singular matrices.

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Similar questions

Q. The matrix

[\begin{matrix} 5 & 10 & 3 \\ - 2 & - 4 & 6 \\ - 1 & - 2 & b \end{matrix}]

is a singular matrix, if the value of b is
(a) − 3
(b) 3
(c) 0
(d) non-existent

If A, B are square matrices of order 3, A is non-singular and AB = O, then B is a
(a) null matrix
(b) singular matrix
(c) unit-matrix
(d) non-singular matrix

Q. Define a binary operation * on the set {0, 1, 2, 3, 4, 5} as

a * b = \{\begin{cases} a + b & , if a + b < 6 \\ a + b - 6 & , if a + b \geq 6 \end{cases}

Show that 0 is the identity for this operation and each element a ≠ 0 of the set is invertible with 6 − a being the inverse of a.

A matrix ‘B’ is singular if

Q. Assertion :The inverse of the matrix

A = [a_{i j}]_{n \times n}

, where

a_{i j} = 0, i \geq j

B = [a_{i j}^{- 1}]_{n \times n}

Reason: The inverse of singular matrix does not exist.

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