Prove without expanding:


Dear Student,
Please find below the solution to the asked query:

L.H.S.=345121314222324+135231242214624As determinant of matrix and its tranpose is equal , hence we getL.H.S.=345121314222324+131214546232224Interchange C1 and C2 in second determinant and R1 and R2 in first determinant=-121314345222324-121314456222324Interchange R2 and R3 in both determinants=+121314222324345+121314222324456As we two rows are same, hence we can add determinant along third row=1213142223247911=R.H.S. 

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