Grade 12 Matrices

If A and B are square matrices of the same order, then (A + B) (A – B) is equal to

• (A) A² – B²

• (B) A² – BA – AB – B²

• (C) A² – B² + BA – AB

• (D) A² – BA + B² + AB

• (A) only AB is defined

• (B) only BA is defined

• (C) AB and BA both are defined

• (D) AB and BA both are not defined

• (A) scalar matrix

• (B) diagonal matrix

• (C) unit matrix

• (D) square matrix

If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a

• (A) Skew symmetric matrix

• (B) Null matrix

• (C) Symmetric matrix

• (D) None of these

If A and B are two skew symmetric matrices of same order, then AB is symmetric matrix if

If two matrices A and B are of the same order, then 2A + B = B + 2A.

• True

• False

For the non singular matrix A, (A′) –1 = (A–1)′.

• True
• False

Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is

• (A) 9

• (B) 27

• (C) 81

• (D) 512

A – B is equal to

• (A) I

• (B) O

• (C) 2I

If A and B are two matrices of the order 3 × m and 3 × n, respectively, and m = n, then the order of matrix (5A – 2B) is

• (A) m × 3

• (B) 3 × 3

• (C) m × n

• (D) 3 × n