If A is a square matrix such that A2=I, then find the simplified value of (A−I)3+(A+I)3−7A.
Statement 1: Matrix 3×3,aij=i+2ji−j cannot be expressed as a sum of symmetric and skew-symmetric matrix. Statement 2: Matrix 3×3,aij=i+2ji−j is neither symmetric nor skew-symmetric
A and B are square matrices and A is non-singular matrix, then (A−1BA)n,n∈I′ ,is equal to (A) A−nBnAn (B) AnBnA−n (C) A−1BnA (D) A−nBAn
Statement 1: If f(α)=⎣⎡cosαsinα0−sinαcosα0001⎦⎤,then [F(α)]−1=F(−α)˙ Statement 2: For matrix G(β)=⎣⎡cosβ0−sinβ010sinβ0cosβ⎦⎤˙ we have [G(β)]−1=G(−β)˙
Statement 1: The determinant of a matrix A=([aij])5×5whereaij+aji=0 for all iandj is zero. Statement 2: The determinant of a skew-symmetric matrix of odd order is zero
Each question has four choices a, b, c and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2.
Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1.
Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1.
STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
STATEMENT 1 is FALSE and STATEMENT 2 is TRUE.