[" () Example 1: The number of "2times2" matrices "A=[[a,b],[" for which "]],[qquad [[a,b],[c,d]]^(-1)=[[1/a,1/b],[1/c,1/d]],(a,b,c,d in R)" is "]

The number of 2xx2 matrices A=[[a,bc,d]][[a,bc,d]]^(-1)=[[(1)/(a),(1)/(b)(1)/(c),(1)/(d)]],(a,b,c,d in R) is

Consider the matrices A=[[1,-2],[-1,3]] and B=[[a,b],[c,d]] If AB=[[2,9],[5,6]] , find the values of a,b,c,d

The number of matrices A = [(a,b),(c,d)] ( where a,b,c,d in R ) such that A^(-1) = -A is :

If D=[[1,a,b],[1,b,c],[1,c,a]] , then [[a,b,c],[b,c,a],[1,1,1]] =

If a,b,c,d are in continued proportion then show that abcd(1/a+1/b+1/c+1/d)^2 = (a+b+c+d)^2 .

If D=|(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab)| , then D is -

match the columns (a) a -4, b-2,c-5,d-1 (b) a-4,b-5,c-2,d-1 (c) a-4,b-5,c-1,d-2 (d) a-5, b-4,c-1,d-2

Compute the products A B and B A whichever exists in each of the following cases: A=[1\ -1\ \ 2\ \ 3] and B=[[0],[ 1],[ 3],[ 2]] (ii) [a\ \ b][[c],[ d]]+[a\ \ b\ \ c\ \ d][[a],[ b],[ c],[ d]]

Consider the matrices : A=Consider the matrices : A=[(1,-2),(-1,3)] and B=[(a,b),(c,d)] If AB=[(2,9),(5,6)] , find the values of a,b,c and d.