If A and B are two square matrices such that `B=-A^(-1)BA`, then `(A+B)^(2)` is equal to

A and B are two square matrices such that A^(2)B=BA and if (AB)^(10)=A^(k)B^(10) , then k is

If Aa n dB are two non-singular matrices such that A B=C ,t h e n|B| is equal to (|C|)/(|A|) b. (|A|)/(|C|) c. |C| d. none of these

If A and B are square matrices such that AB = BA then prove that A^(3)-B^(3)=(A-B) (A^(2)+AB+B^(2)) .

If A and B are two matrices of order 3 such that AB=O and A^(2)+B=I , then tr. (A^(2)+B^(2)) is equal to ________.

if Aa n dB are squares matrices such that A^(2006)=Oa n dA B=A+B ,t h e n"det"(B) equals 0 b. 1 c. -1 d. none of these

if A and B are two matrices of order 3xx3 so that AB=A and BA=B then (A+B)^7=

If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB^(n)=B^(n)A . Further, prove that (AB)^(n)=A^(n)B^(n) for all n in N .

If A and B are two invertible matrices of the same order, then adj (AB) is equal to

If A and B are two square matrices of order 3xx3 which satify AB=A and BA=B , then (A+I)^(5) is equal to (where I is idensity matric)