#matrix order

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

If ABᵀ is defined as a square matrix then what is the order of the matrix B, where matrix A has order 2 × 3.

We know that complete solution: write formula, plug data, do arithmetic. Final value matches 2 × 3. Simple and accurate.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 1

If a matrix has p elements, where is p a prime then what is the number of possible orders it can have ?

The logic is straightforward: total elements p=m×n. If p prime, only factor pairs 1×p and p×1. So 2 orders possible. Complete factorization logic.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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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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