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-1A)B = (A-1A)C
⇒ IB=IC
⇒ B=C
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then A=?
If A=
is not invertible then λ=?
Find the adjoint of the matrix 
and hence show that A(adj A) = |A| I3.
