#matrix multiplication

Matrices and Determinants 3

Let A be any m×n matrix, then A² can be found only when

From the definition, solving fully: apply relevant formula, put numbers, compute. Result comes as m = n. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 3

Which of the following condition is incorrect for matrix multiplication?

Here's the idea in simple terms: using formula we get AB = BA. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get AB = BA.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 2

If A=bmatrix 1& 3 5& 2bmatrix and B=bmatrix 3&2 1& 3bmatrix , then |AB| = ?

Applying the basic concept, using formula we get -91. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get -91.

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

Let det M denotes the determinant of the matrix M. Let A and B be 3 × 3 matrices with det A = 3 and det B = 4. Then the

Here's the idea in simple terms: formula det(kA)=k³detA for 3×3. So det(2AB)=2³·detA·detB=8×3×4=96. Complete calculation step by step.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 1

Consider the following question and decide which of the statements is sufficient to answer the question. Find the value

We know that B is identity matrix, so AB=A holds for any A. No value of n appears, both statements insufficient to find n. Complete check shows data missing.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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General Mathematics 1

If A = [ array*20c 0&1 1&0 array ] , then the value of A⁴ is

We know that A=[[0,1],[1,0]]. Calculate A²=I₂. Then A⁴=(A²)²=I. Complete solution identity matrix.

Ref: NCERT Mathematics Class XI and XII

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Matrices and Determinants 1

lf the order of A is 4 × 3, the order of B is 4 × 5 and the order of C is 7 × 3, then the order of (AᵀB)ᵀ C ᵀ is

The trick is Aᵀ is 3×4, so AᵀB is 3×5. Then (AᵀB)ᵀ is 5×3. Cᵀ is 3×7. Multiply 5×3 with 3×7 =5×7. Final order 5×7.

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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