(A) Given that $A$ is a non-singular matrix,its determinant $|A| \neq 0$,which implies that the inverse matrix $A^{-1}$ exists. Given the equation $AB

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(A) Given that $A$ is a non-singular matrix,its determinant $|A| \neq 0$,which implies that the inverse matrix $A^{-1}$ exists. Given the equation $AB = O$,where $O$ is the zero matrix. Multiplying both sides by $A^{-1}$ on the left: $A^{-1}(AB) = A^{-1}O$ $(A^{-1}A)B = O$ $IB = O$ $B = O$ Therefore,$B$ must be a null matrix.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Types of matrices, Algebra of matrices

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If $A$ and $B$ are square matrices of order $3 \times 3$,$A$ is non-singular,and $AB = O$,then $B$ is a:

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null matrix
B
non-singular matrix
C
singular matrix
D
unit matrix

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3 and 4 .Determinants and Matrices

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Types of matrices, Algebra of matrices

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If $A$ and $B$ are square matrices of order $3 \times 3$,$A$ is non-singular,and $AB = O$,then $B$ is a:

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