If M is a `3xx3` matrix, where det `M=1` and `M M^(T)=I`, where `'I'` is an identity matrix, then prove that det. `(M-I)=0`.

If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an identity matrix, prove theat det (M-I)=0.

Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0 .

If A = [(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisfying the equation "AA"^(T) = 9I , where I is 3xx3 identity matrix, then the ordered pair (a,b) is equal to

If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is an identity matrix of same order as of A )

A square matrix P satisfies P^(2)=I-P where I is identity matrix. If P^(n)=5I-8P , then n is

Let A be a 2 xx 2 matrix with non-zero entries and let A^2=I, where i is a 2 xx 2 identity matrix, Tr(A) i= sum of diagonal elements of A and |A| = determinant of matrix A. Statement 1:Tr(A)=0 Statement 2: |A| =1

A square matrix M of order 3 satisfies M^(2)=I-M , where I is an identity matrix of order 3. If M^(n)=5I-8M , then n is equal to _______.

If A is a square matrix such that A^(3)=I , then prove that A is non-singular

If A is a matrix of order 3, then det (kA) …………….