Q. 975.0( 1 Vote )

# Which of the following statements are True or False

If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

Answer :

False

∵ If AB = AC => B=C

The above condition is only possible if matrix A is invertible

(i.e |A|≠0).

⇒ If A is invertible, then

⇒ A^{-1(}AB)= A^{-1(}AC)

⇒ (A^{-1}A)B = (A^{-1}A)C

⇒ IB=IC

⇒ B=C

Rate this question :

Which of the following statements are True or False

If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

Mathematics - ExemplarWhich of the following statements are True or False

If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

Mathematics - ExemplarUsing matrices solve the following system of equations.

3x + 4y + 7z = 4

2x – y + 3z = –3

x + 2y – 3z = 8

Mathematics - Board PapersUsing matrices, solve the following system of equations:

2x - 3y + 5z = 11

3x + 2y - 4z = -5

x + y - 2z = -3

Mathematics - Board PapersUsing matrices solve the following system of equations:

x + y – z = 3; 2x + 3y + z = 10; 3x – y – 7z = 1

Mathematics - Board PapersIf A is an invertible matrix and A^{-1} = then A=?

If A=is not invertible then λ=?

RS Aggarwal - MathematicsFind the adjoint of the matrix and hence show that A(adj A) = |A| I_{3}.