Answer:
We shall prove the
result by mathematical induction.
For n = 1
L.H.S. = (aI + bA)? = aI + bA
R.H.S. = anI + nan?1bA
given result is
true for n =1.
Let us suppose that given statement
is true for n = k.
?.(1)
Consider for n = k +1
(aI + bA)k+1 = (aI + bA)k.
(aI + bA)
= (akI + kak?1
bA) (aI + bA)
[Using (1)]
= ak+1I + akbIA
+ akba AI
+ kb2 ak?1A2
which is true for n = k + 1.
Hence by P.M.I., given statement is
true for
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