#nonsingular matrix

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Matrices and Determinants 2

Consider two matrices M₁ and M₂ with M₁*M₂ = 0 and M₁ is non singular. Then which of the following is true?

Applying the basic concept, we verify M₂ is null matrix by full calculation: use standard identity, substitute, simplify step by step to reach M₂ is null matrix.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 1

If A and B are two n x n non singular matrix, then _____________

Recall the rule non-singular means |A|≠0,|B|≠0. Formula |AB|=|A||B|≠0. So AB also non-singular, inverse exists. Complete reasoning.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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#nonsingular matrix

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Consider two matrices M₁ and M₂ with M₁*M₂ = 0 and M₁ is non singular. Then which of the following is true?

If A and B are two n x n non singular matrix, then _____________

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