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Write the number of all possible matrices of order `2xx2` with each entry 1, 2 or 3.

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To find the number of all possible matrices of order \(2 \times 2\) with each entry being either 1, 2, or 3, we can follow these steps: ### Step 1: Understand the Structure of the Matrix A \(2 \times 2\) matrix has 2 rows and 2 columns. Therefore, it contains a total of 4 elements. We can denote the matrix as follows: \[ \begin{pmatrix} a_{11} & a_{12} \\ ...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If [x+y x-y]=[2 1 4 3][1-2] , then write the value of (x ,\ y) .

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  2. Matrix A=[0 2b-2 3 1 3 3a3-1] is given to be symmetric, find the value...

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  3. Write the number of all possible matrices of order 2xx2 with each e...

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  4. If [2\ \ 1\ \ 3][-1 0-1-1 1 0 0 1 1][1 0-1]=A , then write the order o...

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  5. If A=[3 5 7 9] is written as A=P+Q , where P is symmetric and Q is sk...

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  6. If A=[(1 ,0, 0),(0, 1,0),( a,b, -1)] , then A^2 is equal to (a) a n...

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  7. If A=[i0 0i],\ n in N , then A^(4n) equals [0i i0] (b) [0 0 0 0] (c) ...

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  8. If A and B are two matrices such that A B=A and B A=B , then B^...

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  9. If A B=A and B A=B , where A and B are square matrices, then B^2=B ...

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  10. If A and B are two matrices such that AB=B and BA=A , then A^2+B^2=

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  11. If [(cos\ (2pi)/7,-sin\ (2pi)/7),(sin\ (2pi)/7,cos\ (2pi)/7)]^k=[(1,0)...

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  12. If the matrix A B is zero, then It is not necessary that either A=O...

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  13. Let A=[(a,0, 0),( 0,a,0),( 0, 0,a)] , then A^n is equal to [(a^n,0,...

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  14. If A ,\ B are square matrices of order 3,\ A is non-singular and A ...

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  15. If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a1,a2,a3),(b1,b2,b3),(c1,c2...

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  16. If A=[(1,a),(0, 1)] , then A^n (where n in N) equals [(1,n a),(0,...

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  17. If A=[1 2x0 1 0 0 0 1] and B=[1-2y0 1 0 0 0 1] and A B=I3 , then x+y e...

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  18. If A=[1-1 2-1] , B=[a1b-1] and (A+B)^2=A^2+B^2 , then values of a and ...

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  19. If A=[alphabetagamma-alpha] is such that A^2=I , then 1+alpha^2+betaga...

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  20. If S=[S(i j)] is a scalar matrix such that s(i i)=ka n dA is a square ...

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