#identity matrix

Matrices and Determinants 3

If A = ;[ array*20c 1& 1 4& 6 array ] , find k so that A^2 = kA - 2I , where I is an identity matrix.

From the definition, after simplifying, 7 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 3

If A = [ array*20c & - & array ] , then for what value of α, A is an identity matrix?

We know that solving fully: apply relevant formula, put numbers, compute. Result comes as 90°. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 3

Consider the following statements: 1. Every zero matrix is a square matrix. 2. A matrix has a numerical value. 3. A unit

The logic is straightforward: using formula we get 3 only. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get 3 only.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 2

If A is a square matrix such that A² = I, then A³ + (A + I)² - 9A - I2 - A2 is

Look at it this way: we verify -6A by full calculation: use standard identity, substitute, simplify step by step to reach -6A.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 2

If A = [ array*20c 2θ & - 2θ 2θ & 2θ array ] and A + Aᵀ = I Where I is the unit matrix of 2 × 2 & Aᵀ is the transpose of

In easy words, after simplifying, 6 is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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