Q. 32 B5.0( 1 Vote )

# Let and a = 4, b = –2.

Show that:

A(BC) = (AB)C

Answer :

To prove: A(BC) = (AB)C

LHS = A(BC) =

⇒ LHS =

⇒ LHS =

⇒ LHS =

RHS = (AB)C =

Performing matrix multiplication as done for LHS

⇒ RHS =

⇒ RHS =

Clearly LHS = RHS =

∴ A(BC) = (AB)C …proved

Rate this question :

If then the value of x + y is

Mathematics - ExemplarSolve for x and y:

Mathematics - Exemplar

Which of the following statements are True or False

If A and B are two square matrices of the same order, then AB = BA.

Mathematics - ExemplarIf AB = BA for any two square matrices, prove by mathematical induction that (AB)^{n} = A^{n} B^{n}.

If and , then verify (BA)^{2} ≠ B^{2}A^{2}.

Compute the following sums:

RD Sharma - Volume 1

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

Mathematics - ExemplarThe matrix is a

Mathematics - ExemplarShow by an example that for A ≠ O, B ≠ O, AB = O.

Mathematics - ExemplarIf , and , verify:

(i) (AB) C = A (BC)

(ii) A(B + C) = AB + AC

Mathematics - Exemplar