EASY
12th West Bengal Board
IMPORTANT
Earn 100

If A and B are two square matrices such that AB=B and BA=A; then show that A and B both are idempotent.

Important Questions on Elementary Theory of Matrices

MEDIUM
12th West Bengal Board
IMPORTANT
Show that 224134123 is idempotent.
HARD
12th West Bengal Board
IMPORTANT

Express each of the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix

323453245

HARD
12th West Bengal Board
IMPORTANT

Express each of the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix

3    2    54    1    30    6    7

HARD
12th West Bengal Board
IMPORTANT

Express each of the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix

341230145

MEDIUM
12th West Bengal Board
IMPORTANT

Express the following matrix as the sum of a symmetric and a skew-symmetric matrix 135-683-465

MEDIUM
12th West Bengal Board
IMPORTANT
If A=011434334, then show that A2=I3.
MEDIUM
12th West Bengal Board
IMPORTANT
If A=3    41    1 and n be a positive integer, then prove that An=1+2n4nn12n.
MEDIUM
12th West Bengal Board
IMPORTANT
Show that λ    10    λn=λnnλn10λn(λ0) for any +ve integer n. Hence obtain the value of A51, where A=1101.