#square matrix

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

View Details

Matrices and Determinants 3

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

View Details

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

View Details

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

View Details