If `m=[[1,0],[0,1]]`and `n=[[0,1],[-1,0]]`, then what is the value of the determinant of `mcostheta- nsintheta`

If m=[{:(1,0),(0,1):}] and n=[{:(0,1),(-1,0):}] , then what is the value of the determinant of m cos theta - n sin theta ?

If A = ((1,2),(2,3))and = ((1,0),(1,0)) , then what is the value of determinant of AB ?

if |[1,0,0],[0,1,0],[0,0,1]|=|[0,0,1],[0,1,0],[x,0,1]| then what is the value of x?

What is PH value of 0.1 N HCl?

Let A = [{:(1,0),(0,-1):}]and B =[{:(1,x),(0,1):}] If AB = BA, then what is the value of x ?

If [(0, 1), (-1,0)]^n = [(1,0),(0, 1)] then the value of n is

Let A=[{:(1,0),(0,-1):}] and B=[{:(1,x),(0,1):}] . If AB=BA then what is the value of x ?

If A= [[0,1,0],[1,0,0],[0,0,1]] , then A^(2n)= where n is a positive integer.

If A=[[1,1],[0,1]] , prove that A^n=[[1,n],[0,1]] for all n epsilon N

Consider two matrices B=[[1,0],[0,-1]] and C=[[0,1],[-1,0]]. If matrix A=sum_(n=1)^(100)(B^(n)+C^(n)) ,then find the absolute value of determinant of matrix A.