Let M and N be two `3xx3` matrices such that `MN=NM`. Further, if `M ne N^(2)` and `M^(2)=N^(4)`, then

Let m and N be two 3x3 matrices such that MN=NM. Further if M!=N^2 and M^2=N^4 then which of the following are correct.

Let Ma n dN be two 3xx3 non singular skew-symmetric matrices such that M N=N Mdot If P^T denote the transpose of P , then M^2N^2(M^T N^(-1))^T is equal to M^2 b. -N^2 c. -M^2 d. M N

Let M and N are two non singular matrices of order 3 with real entries such that (adjM)=2N and (adjN)=M . If MN=lambdaI , then the value the values of lambda is equal to (where, (adj X) represents the adjoint matrix of matrix X and I represents an identity matrix)

If A and B are two matrices of the order 3 xx m and 3 xx n , respectively and m= n, then order of matrix (5A-2B) is (a) m xx 3 (b) 3 xx 3 (c) m xx n (d) 3 xx n

If A and B are two matrices of the order 3 xx m and 3 xx n , respectively and m= n, then order of matrix (5A-2B) is (a) m xx 3 (b) 3 xx 3 (c) m xx n (d) 3 xx n

Let M be a 3xx3 matrix satisfying M^(3)=0 . Then which of the following statement(s) are true: (a) |M^(2)+M+I|ne0 (b) |M^(2)-M+I|=0 (c) |M^(2)+M+I|=0 (d) |M^(2)-M+I|ne0

Prove that (mn)! Is divisible by (n!)^(m) " and" (m!)^(n)

If A and B are two matrices of order 3 xx m and 3 xx n respectively, and m = n, then the order of matrix (5A - 2B) is

Prove that (mn)! Is divisible by (n!)^(m) " and" (m!)^(n) .