Class 12 Maths Determinants Singular & Non Singular Matrix

Singular Matrix

A square matrix A is said to be singular if |A| = 0.  

   

Non Singular Matrix

A square matrix A is said to be non-singular if |A| ≠ 0

 

Theorem:  If A and B are nonsingular matrices of the same order, then AB and BA are also nonsingular matrices of the same order

Theorem: If A and B are non-Zero Matrices of the same order, then AB and BA can be Zero Matrix

Theorem: The determinant of the product of matrices is equal to product of their respective determinants, that is, |AB| = |A| * |B| , where A & B are square matrices of same order

 

Theorem: A square matrix A is invertible if and only if A is nonsingular matrix

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