If `M` is a `3 xx 3` matrix, where det `M=1 and MM^T=1,` where `I` is an identity matrix, prove theat det `(M-I)=0.`

If M is a 3xx3 matrix such that M^(2)=O , then det. ((I+M)^(50)-50M) where I is an identity matrix of order 3, is equal to:

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

if for a matrix A, A^2+I=O , where I is the identity matrix, then A equals

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

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 )

If A is skew symmetric matrix, then I - A is (where I is identity matrix of the order equal to that of A)

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

If P is a 3xx3 matrix such that P^T = 2P+I , where P^T is the transpose of P and I is the 3xx3 identity matrix, then there exists a column matrix, X = [[x],[y],[z]]!=[[0],[0],[0]] such that

If A=[1 2 2 2 1-2a2b] is a matrix satisfying the equation AA^T=""9I , where I is 3xx3 identity matrix, then the ordered pair (a, b) is equal to : (1) (2,-1) (2) (-2,""1) (3) (2, 1) (4) (-2,-1)

A square m atrix where every element is unity is called an identity matrix.