Matrices - Class 10 MCQ

Rows = 2 (two horizontal lines).

Columns = 3 (three vertical lines).

Order = 2 x 3

Total elements = rows × columns
= 4 × 5
= 20

All elements are 0.
By definition, such a matrix = Zero (Null) Matrix.

For equality, corresponding elements must match.
So, x = 4.

= 

= 

= 

Add corresponding entries (same order 2 × 3)

Row 1: (2 + 1, −1+ 2, 0 + 3) = (3, 1, 3).

Row 2: (3 + 0, 4 + (−1), 1 + 2) = (3, 3, 3).

Rearrange: X = B − A.

Compute: 

Multiply row-by-column.

Compute BA (order matters!).

Since AB ≠ BA, multiplication is not commutative.

Sum = A² − 3A + 2I = 

= 

Each column of B is the same; each row of A sums to 0.

Dot products: 1⋅5 + (−1)⋅5 = 0, 2⋅5 + (−2)⋅5 = 0.

Hence, AB = O (zero matrix), though A, B ≠ O.

Identity property: A⋅I = I⋅A = A.
Multiplying by I keeps every entry unchanged.