If A is a square matrix of order 3 and |A| = 4, then |2A| equals
Notice that we verify 32 by full calculation: use standard identity, substitute, simplify step by step to reach 32.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
Matrices and Determinants 3
This category gathers practice questions centered on matrices and determinants. It covers operations, properties, and problem‑solving techniques useful for higher‑level linear algebra topics.
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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
If A is any square matrix, then
Let's break it down: we verify A+At is symmetric by full calculation: use standard identity, substitute, simplify step by step to reach A+At is symmetric.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If A and B are two matrices such that AB = A and BA = B, then which one of the following is correct?
Look at it this way: complete solution: write formula, plug data, do arithmetic. Final value matches (Aᵀ)² = Aᵀ. Simple and accurate.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
The Inverse of the Matrix is Possible only for
The trick is after simplifying, Non-Singular Matrix is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
Which of the following conditions holds true for a skew-symmetric matrix?
Understanding this is easy: using formula we get A = -A’. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get A = -A’.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
Which of the following is not the property of transpose of a matrix?
Look at it this way: solving fully: apply relevant formula, put numbers, compute. Result comes as (AB) ’= (BA)’. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
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
Which of the following relations is symmetric but neither reflexive nor transitive for a set A = 1, 2, 3.
Think of it like this: using formula we get R = (1, 2), (2, 1). Calculation gives this directly, check steps: apply rule, substitute values, simplify to get R = (1, 2), (2, 1).
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If A, B are square matrices of the same order and B is a skew-symmetric matrix, then A′BA is:
We know that using formula we get Skew-Symmetric matrix.. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get Skew-Symmetric matrix..
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If A=bmatrix x & 2 4 & 3 bmatrix and A ^-1=bmatrix 18 & -1 12 -1 6& 4 9 bmatrix , then find the value of x?
Applying the basic concept, solving fully: apply relevant formula, put numbers, compute. Result comes as 32 3. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If A = [ array*20c 1&3 + x&2 1 - x&2&y + 1 2&5 - y&3 array ] is a symmetric matrix, then 3x + y is equal to?
We can see that after simplifying, -1 is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
