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.`

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.

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

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

If A is a skew-symmetric matrix of order 3, then prove that det A = 0 .

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

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 _______.

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h e r eI is the unit matrix of the name order as that of A , then th value of |9alpha| is equal to ________.