If `A=d i ag\ (a\ \ b\ \ c)` , show that `A^n=d i ag\ (a^n\ \ b^n\ \ c^n)` for all positive integer `n` .

If A=d i ag(abc), show that A^n=d i ag(a^nb^nc^n) for all positive integer n .

If A=diag(abc), show that A^(n)=diag(a^(n)b^(n)c^(n)) for all positive integer n.

If A=diag(abc), show that A^(n)=diag(a^(n)b^(n)c^(n)) for all positive integer n .

If A=diag[a,b,c] then show that A^(n)=diag[a^(n),b^(n),c^(n)] for all n in N

If Aa n dB are square matrices of the same order and A is non-singular, then for a positive integer n ,(A^(-1)B A)^n is equal to A^(-n)B^n A^n b. A^n B^n A^(-n) c. A^(-1)B^n A^ d. n(A^(-1)B^A)^

If Aa n dB are square matrices of the same order and A is non-singular, then for a positive integer n ,(A^(-1)B A)^n is equal to A^(-n)B^n A^n b. A^n B^n A^(-n) c. A^(-1)B^n A^ d. n(A^(-1)B^A)^

If A and B are square matrices of the same order and A is non-singular,then for a positive integer n,(A^(-1)BA)^(n) is equal to A^(-n)B^(n)A^(n) b.A^(n)B^(n)A^(-n) c.A^(-1)B^(n)A d.n(A^(-1)BA)

Let A ,\ B be two matrices such that they commute. Show that for any positive integer n , (A B)^n=A^n B^n

Prove that the Binomial theorem (a + b)^(n) = ""^(n)C_(0)a^(n) + ""^(n)C_(1)a^(n - 1)b + ""^(n)C_(2)a^(n - 2)b^(2) + .. ""^(n)C_(n)b^(n) for any positive integer 'n'.

(x+1) is a factor of x^n+1 only if (a)n is an odd integer (b) n is an even integer (c )n is a negative integer (d)n is a positive integer