Let A and B be two square matrices of order 2. If $$det\,(A) = 2$$, $$det\,(B) = 3$$ and $$\det \left( {(\det \,5(det\,A)B){A^2}} \right) = {2^a}{3^b}{5^c}$$ for some a, b, c, $$\in$$ N, then a + b + c is equal to :

Let $$A = \left( {\matrix{ 2 & { - 1} \cr 0 & 2 \cr } } \right)$$. If $$B = I - {}^5{C_1}(adj\,A) + {}^5{C_2}{(adj\,A)^2} - \,\,.....\,\, - {}^5{C_5}{(adj\,A)^5}$$, then the sum of all elements of the matrix B is

If the system of linear equations

2x + y $$-$$ z = 7

x $$-$$ 3y + 2z = 1

x + 4y + $$\delta$$z = k, where $$\delta$$, k $$\in$$ R has infinitely many solutions, then $$\delta$$ + k is equal to:

Let $$A = [{a_{ij}}]$$ be a square matrix of order 3 such that $${a_{ij}} = {2^{j - i}}$$, for all i, j = 1, 2, 3. Then, the matrix A² + A³ + ...... + A¹⁰ is equal to :