can you please help me with this

Question 1 [2x3pts] a. Let A and B be nonsingular N x N matrices. Show that (AB)-1= B-IA-1. b. Let A and B be Nx N matrices; let C=AB. Starting from the definition of a matrix multiplication, cu = Ek dubaje show that (AB) = BTAT. Question 2 [2x3pts] a. Consider the N x N matrices U. V. E. U(V) is made up of N-dimensional column vectors [u,) ( ), E is a diagonal matrix with elements (o ]. Consider the matrix M = UCV , write out M explicitly in terms of (u) ((v) ) and (o ). b. Consider the real N x N matrix S, which is made up of N-dimensional column vectors (5, ). Suppose that { } are such that My, = list for the N x N matrix M; furthermore, the (5, } have the property if i = j if i # j Consider the matrix A = S'MS write out A explicitly in terms of the (5{ } and (; ]. Question 3 [3x3pts] ZA ZE Consider the alternating current (AC) RLC circuit above. {ZA. Za, Zc. Zo. ZE) are the impedances of their respective circuits elements, (Va. V,) denotes the magnitudes of AC voltages sources (with the same frequency). [Note: each element can be resistor, inductor, or capacitor). The amplitudes of the currents (1, 12. I;] are determined by (ZA + ZB)h - ZBl2 = Va -Zghi + (ZB + Zc + Zp)/2 - Zola = 0 -Zplz + (ZD + ZE)3 = -Vo