#square matrices

Matrices and Determinants 2

If A, B, C are square matrices of the same order, then which of the following is true?

Applying the basic concept, using formula we get AB = I ⇒ AB = BA. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get AB = I ⇒ AB = BA.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 2

From the matrix equation AB = AC, where A, B, C are the square matrices of same order, we can conclude B = C provided

Think of it like this: complete solution: write formula, plug data, do arithmetic. Final value matches A is non-singular. Simple and accurate.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 2

The sum and product of matrices A and B exist. Which of the following implications are necessarily true? I. A and B are

We can see that after simplifying, Only I is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 1

Multiplication of real valued square matrices of same dimension is:

Applying the basic concept, square matrices multiplication is associative: (AB)C=A(BC). Check: A(BC) and (AB)C give same result. Not commutative, AB may not equal BA. So A correct.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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