The number of `2 xx 2` matrices `A=[(a,b),(c,d)]` for which `[(a,b),(c,d)]^-1=[(1/a,1/b),(1/c,1/d)],(a,b,c,d in R)` is

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

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.

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.

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

Let S be the set of 2xx2 matrices given by S={A=[[a,b],[c,d]],"where" a,b,c,d,in I} , such that A^(T)=A^(-1) Then

Let S be the set of 2xx2 matrices given by S={A=[[a,b],[c,d]],"where" a,b,c,d,in I} , such that A^(T)=A^(-1) Then

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

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 .